[{"publication":"Transactions of the American Mathematical Society","issue":"9","abstract":[{"text":"<p>This paper is the first in a series of two dedicated to the study of period relations of the type <disp-formula content-type=\"math/mathml\">\r\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L left-parenthesis one half plus k comma normal upper Pi right-parenthesis element-of left-parenthesis 2 pi i right-parenthesis Superscript d dot k Baseline normal upper Omega Subscript left-parenthesis negative 1 right-parenthesis Sub Superscript k Subscript Baseline reverse-solidus bf upper Q left-parenthesis normal upper Pi right-parenthesis comma one half plus k critical comma\">\r\n  <mml:semantics>\r\n    <mml:mrow>\r\n      <mml:mi>L</mml:mi>\r\n      <mml:mstyle scriptlevel=\"0\">\r\n        <mml:mrow class=\"MJX-TeXAtom-ORD\">\r\n          <mml:mo maxsize=\"1.623em\" minsize=\"1.623em\">(</mml:mo>\r\n        </mml:mrow>\r\n      </mml:mstyle>\r\n      <mml:mfrac>\r\n        <mml:mn>1</mml:mn>\r\n        <mml:mn>2</mml:mn>\r\n      </mml:mfrac>\r\n      <mml:mo>+</mml:mo>\r\n      <mml:mi>k</mml:mi>\r\n      <mml:mo>,</mml:mo>\r\n      <mml:mi mathvariant=\"normal\">Π<!-- Π --></mml:mi>\r\n      <mml:mstyle scriptlevel=\"0\">\r\n        <mml:mrow class=\"MJX-TeXAtom-ORD\">\r\n          <mml:mo maxsize=\"1.623em\" minsize=\"1.623em\">)</mml:mo>\r\n        </mml:mrow>\r\n      </mml:mstyle>\r\n      <mml:mspace width=\"thickmathspace\" />\r\n      <mml:mo>∈<!-- ∈ --></mml:mo>\r\n      <mml:mspace width=\"thickmathspace\" />\r\n      <mml:mo stretchy=\"false\">(</mml:mo>\r\n      <mml:mn>2</mml:mn>\r\n      <mml:mi>π<!-- π --></mml:mi>\r\n      <mml:mi>i</mml:mi>\r\n      <mml:msup>\r\n        <mml:mo stretchy=\"false\">)</mml:mo>\r\n        <mml:mrow class=\"MJX-TeXAtom-ORD\">\r\n          <mml:mi>d</mml:mi>\r\n          <mml:mo>⋅<!-- ⋅ --></mml:mo>\r\n          <mml:mi>k</mml:mi>\r\n        </mml:mrow>\r\n      </mml:msup>\r\n      <mml:msub>\r\n        <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi>\r\n        <mml:mrow class=\"MJX-TeXAtom-ORD\">\r\n          <mml:mo stretchy=\"false\">(</mml:mo>\r\n          <mml:mo>−<!-- − --></mml:mo>\r\n          <mml:mn>1</mml:mn>\r\n          <mml:msup>\r\n            <mml:mo stretchy=\"false\">)</mml:mo>\r\n            <mml:mi>k</mml:mi>\r\n          </mml:msup>\r\n        </mml:mrow>\r\n      </mml:msub>\r\n      <mml:mrow class=\"MJX-TeXAtom-ORD\">\r\n        <mml:mtext>\\bf Q</mml:mtext>\r\n      </mml:mrow>\r\n      <mml:mo stretchy=\"false\">(</mml:mo>\r\n      <mml:mi mathvariant=\"normal\">Π<!-- Π --></mml:mi>\r\n      <mml:mo stretchy=\"false\">)</mml:mo>\r\n      <mml:mo>,</mml:mo>\r\n      <mml:mspace width=\"1em\" />\r\n      <mml:mfrac>\r\n        <mml:mn>1</mml:mn>\r\n        <mml:mn>2</mml:mn>\r\n      </mml:mfrac>\r\n      <mml:mo>+</mml:mo>\r\n      <mml:mi>k</mml:mi>\r\n      <mml:mspace width=\"thickmathspace\" />\r\n      <mml:mtext>critical</mml:mtext>\r\n      <mml:mo>,</mml:mo>\r\n    </mml:mrow>\r\n    <mml:annotation encoding=\"application/x-tex\">\\begin{equation*} L\\Big (\\frac {1}{2}+k,\\Pi \\Big )\\;\\in \\;(2\\pi i)^{d\\cdot k}\\Omega _{(-1)^k}\\textrm {\\bf Q}(\\Pi ),\\quad \\frac {1}{2}+k\\;\\text {critical}, \\end{equation*}</mml:annotation>\r\n  </mml:semantics>\r\n</mml:math>\r\n</disp-formula>\r\n for certain automorphic representations <inline-formula content-type=\"math/mathml\">\r\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Pi\">\r\n  <mml:semantics>\r\n    <mml:mi mathvariant=\"normal\">Π<!-- Π --></mml:mi>\r\n    <mml:annotation encoding=\"application/x-tex\">\\Pi</mml:annotation>\r\n  </mml:semantics>\r\n</mml:math>\r\n</inline-formula> of a reductive group <inline-formula content-type=\"math/mathml\">\r\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G period\">\r\n  <mml:semantics>\r\n    <mml:mrow>\r\n      <mml:mi>G</mml:mi>\r\n      <mml:mo>.</mml:mo>\r\n    </mml:mrow>\r\n    <mml:annotation encoding=\"application/x-tex\">G.</mml:annotation>\r\n  </mml:semantics>\r\n</mml:math>\r\n</inline-formula> In this paper we discuss the case <inline-formula content-type=\"math/mathml\">\r\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G equals normal upper G normal upper L left-parenthesis n plus 1 right-parenthesis times normal upper G normal upper L left-parenthesis n right-parenthesis period\">\r\n  <mml:semantics>\r\n    <mml:mrow>\r\n      <mml:mi>G</mml:mi>\r\n      <mml:mo>=</mml:mo>\r\n      <mml:mrow class=\"MJX-TeXAtom-ORD\">\r\n        <mml:mi mathvariant=\"normal\">G</mml:mi>\r\n        <mml:mi mathvariant=\"normal\">L</mml:mi>\r\n      </mml:mrow>\r\n      <mml:mo stretchy=\"false\">(</mml:mo>\r\n      <mml:mi>n</mml:mi>\r\n      <mml:mo>+</mml:mo>\r\n      <mml:mn>1</mml:mn>\r\n      <mml:mo stretchy=\"false\">)</mml:mo>\r\n      <mml:mo>×<!-- × --></mml:mo>\r\n      <mml:mrow class=\"MJX-TeXAtom-ORD\">\r\n        <mml:mi mathvariant=\"normal\">G</mml:mi>\r\n        <mml:mi mathvariant=\"normal\">L</mml:mi>\r\n      </mml:mrow>\r\n      <mml:mo stretchy=\"false\">(</mml:mo>\r\n      <mml:mi>n</mml:mi>\r\n      <mml:mo stretchy=\"false\">)</mml:mo>\r\n      <mml:mo>.</mml:mo>\r\n    </mml:mrow>\r\n    <mml:annotation encoding=\"application/x-tex\">G=\\mathrm {GL}(n+1)\\times \\mathrm {GL}(n).</mml:annotation>\r\n  </mml:semantics>\r\n</mml:math>\r\n</inline-formula> The case <inline-formula content-type=\"math/mathml\">\r\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G equals normal upper G normal upper L left-parenthesis 2 n right-parenthesis\">\r\n  <mml:semantics>\r\n    <mml:mrow>\r\n      <mml:mi>G</mml:mi>\r\n      <mml:mo>=</mml:mo>\r\n      <mml:mrow class=\"MJX-TeXAtom-ORD\">\r\n        <mml:mi mathvariant=\"normal\">G</mml:mi>\r\n        <mml:mi mathvariant=\"normal\">L</mml:mi>\r\n      </mml:mrow>\r\n      <mml:mo stretchy=\"false\">(</mml:mo>\r\n      <mml:mn>2</mml:mn>\r\n      <mml:mi>n</mml:mi>\r\n      <mml:mo stretchy=\"false\">)</mml:mo>\r\n    </mml:mrow>\r\n    <mml:annotation encoding=\"application/x-tex\">G=\\mathrm {GL}(2n)</mml:annotation>\r\n  </mml:semantics>\r\n</mml:math>\r\n</inline-formula> is discussed in part two. Our method is representation theoretic and relies on the author’s recent results on global rational structures on automorphic representations. We show that the above period relations are intimately related to the field of definition of the global representation <inline-formula content-type=\"math/mathml\">\r\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Pi\">\r\n  <mml:semantics>\r\n    <mml:mi mathvariant=\"normal\">Π<!-- Π --></mml:mi>\r\n    <mml:annotation encoding=\"application/x-tex\">\\Pi</mml:annotation>\r\n  </mml:semantics>\r\n</mml:math>\r\n</inline-formula> under consideration. The new period relations we prove are in accordance with Deligne’s Conjecture on special values of <inline-formula content-type=\"math/mathml\">\r\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\">\r\n  <mml:semantics>\r\n    <mml:mi>L</mml:mi>\r\n    <mml:annotation encoding=\"application/x-tex\">L</mml:annotation>\r\n  </mml:semantics>\r\n</mml:math>\r\n</inline-formula>-functions, and the author expects this method to apply to other cases as well.</p>","lang":"eng"}],"extern":"1","date_created":"2024-04-03T16:58:26Z","keyword":["Applied Mathematics","General Mathematics"],"type":"journal_article","title":"On period relations for automorphic 𝐿-functions I","year":"2018","author":[{"first_name":"Fabian","last_name":"Januszewski","orcid":"0000-0002-3184-237X","full_name":"Januszewski, Fabian","id":"81636"}],"publication_identifier":{"issn":["0002-9947","1088-6850"]},"date_updated":"2024-04-03T17:26:38Z","publication_status":"published","intvolume":"       371","article_type":"original","language":[{"iso":"eng"}],"doi":"10.1090/tran/7527","citation":{"ieee":"F. Januszewski, “On period relations for automorphic 𝐿-functions I,” <i>Transactions of the American Mathematical Society</i>, vol. 371, no. 9, pp. 6547–6580, 2018, doi: <a href=\"https://doi.org/10.1090/tran/7527\">10.1090/tran/7527</a>.","apa":"Januszewski, F. (2018). On period relations for automorphic 𝐿-functions I. <i>Transactions of the American Mathematical Society</i>, <i>371</i>(9), 6547–6580. <a href=\"https://doi.org/10.1090/tran/7527\">https://doi.org/10.1090/tran/7527</a>","chicago":"Januszewski, Fabian. “On Period Relations for Automorphic 𝐿-Functions I.” <i>Transactions of the American Mathematical Society</i> 371, no. 9 (2018): 6547–80. <a href=\"https://doi.org/10.1090/tran/7527\">https://doi.org/10.1090/tran/7527</a>.","short":"F. Januszewski, Transactions of the American Mathematical Society 371 (2018) 6547–6580.","mla":"Januszewski, Fabian. “On Period Relations for Automorphic 𝐿-Functions I.” <i>Transactions of the American Mathematical Society</i>, vol. 371, no. 9, American Mathematical Society (AMS), 2018, pp. 6547–80, doi:<a href=\"https://doi.org/10.1090/tran/7527\">10.1090/tran/7527</a>.","bibtex":"@article{Januszewski_2018, title={On period relations for automorphic 𝐿-functions I}, volume={371}, DOI={<a href=\"https://doi.org/10.1090/tran/7527\">10.1090/tran/7527</a>}, number={9}, journal={Transactions of the American Mathematical Society}, publisher={American Mathematical Society (AMS)}, author={Januszewski, Fabian}, year={2018}, pages={6547–6580} }","ama":"Januszewski F. On period relations for automorphic 𝐿-functions I. <i>Transactions of the American Mathematical Society</i>. 2018;371(9):6547-6580. doi:<a href=\"https://doi.org/10.1090/tran/7527\">10.1090/tran/7527</a>"},"status":"public","page":"6547-6580","publisher":"American Mathematical Society (AMS)","_id":"53191","user_id":"81636","volume":371},{"status":"public","user_id":"37888","volume":50,"page":"1053-1064","_id":"48321","publisher":"Springer Science and Business Media LLC","citation":{"chicago":"Wessel, Lena, and Kirstin Erath. “Theoretical Frameworks for Designing and Analyzing Language-Responsive Mathematics Teaching–Learning Arrangements.” <i>ZDM</i> 50, no. 6 (2018): 1053–64. <a href=\"https://doi.org/10.1007/s11858-018-0980-y\">https://doi.org/10.1007/s11858-018-0980-y</a>.","short":"L. Wessel, K. Erath, ZDM 50 (2018) 1053–1064.","ieee":"L. Wessel and K. Erath, “Theoretical frameworks for designing and analyzing language-responsive mathematics teaching–learning arrangements,” <i>ZDM</i>, vol. 50, no. 6, pp. 1053–1064, 2018, doi: <a href=\"https://doi.org/10.1007/s11858-018-0980-y\">10.1007/s11858-018-0980-y</a>.","apa":"Wessel, L., &#38; Erath, K. (2018). Theoretical frameworks for designing and analyzing language-responsive mathematics teaching–learning arrangements. <i>ZDM</i>, <i>50</i>(6), 1053–1064. <a href=\"https://doi.org/10.1007/s11858-018-0980-y\">https://doi.org/10.1007/s11858-018-0980-y</a>","bibtex":"@article{Wessel_Erath_2018, title={Theoretical frameworks for designing and analyzing language-responsive mathematics teaching–learning arrangements}, volume={50}, DOI={<a href=\"https://doi.org/10.1007/s11858-018-0980-y\">10.1007/s11858-018-0980-y</a>}, number={6}, journal={ZDM}, publisher={Springer Science and Business Media LLC}, author={Wessel, Lena and Erath, Kirstin}, year={2018}, pages={1053–1064} }","ama":"Wessel L, Erath K. Theoretical frameworks for designing and analyzing language-responsive mathematics teaching–learning arrangements. <i>ZDM</i>. 2018;50(6):1053-1064. doi:<a href=\"https://doi.org/10.1007/s11858-018-0980-y\">10.1007/s11858-018-0980-y</a>","mla":"Wessel, Lena, and Kirstin Erath. “Theoretical Frameworks for Designing and Analyzing Language-Responsive Mathematics Teaching–Learning Arrangements.” <i>ZDM</i>, vol. 50, no. 6, Springer Science and Business Media LLC, 2018, pp. 1053–64, doi:<a href=\"https://doi.org/10.1007/s11858-018-0980-y\">10.1007/s11858-018-0980-y</a>."},"date_updated":"2024-04-18T09:04:31Z","publication_status":"published","intvolume":"        50","title":"Theoretical frameworks for designing and analyzing language-responsive mathematics teaching–learning arrangements","year":"2018","publication_identifier":{"issn":["1863-9690","1863-9704"]},"author":[{"id":"85190","last_name":"Wessel","first_name":"Lena","full_name":"Wessel, Lena"},{"full_name":"Erath, Kirstin","last_name":"Erath","first_name":"Kirstin"}],"doi":"10.1007/s11858-018-0980-y","language":[{"iso":"eng"}],"issue":"6","publication":"ZDM","keyword":["General Mathematics","Education"],"type":"journal_article","department":[{"_id":"643"}],"date_created":"2023-10-19T09:28:27Z"},{"status":"public","volume":291,"user_id":"58312","_id":"40050","publisher":"Wiley","page":"2516-2535","citation":{"ama":"Baeumer B, Luks T, Meerschaert MM. Space‐time fractional Dirichlet problems. <i>Mathematische Nachrichten</i>. 2018;291(17-18):2516-2535. doi:<a href=\"https://doi.org/10.1002/mana.201700111\">10.1002/mana.201700111</a>","short":"B. Baeumer, T. Luks, M.M. Meerschaert, Mathematische Nachrichten 291 (2018) 2516–2535.","chicago":"Baeumer, Boris, Tomasz Luks, and Mark M. 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Space‐time fractional Dirichlet problems. <i>Mathematische Nachrichten</i>, <i>291</i>(17–18), 2516–2535. <a href=\"https://doi.org/10.1002/mana.201700111\">https://doi.org/10.1002/mana.201700111</a>","ieee":"B. Baeumer, T. Luks, and M. M. Meerschaert, “Space‐time fractional Dirichlet problems,” <i>Mathematische Nachrichten</i>, vol. 291, no. 17–18, pp. 2516–2535, 2018, doi: <a href=\"https://doi.org/10.1002/mana.201700111\">10.1002/mana.201700111</a>."},"intvolume":"       291","publication_status":"published","date_updated":"2023-01-26T17:19:39Z","publication_identifier":{"issn":["0025-584X","1522-2616"]},"author":[{"full_name":"Baeumer, Boris","first_name":"Boris","last_name":"Baeumer"},{"full_name":"Luks, Tomasz","last_name":"Luks","first_name":"Tomasz","id":"58312"},{"full_name":"Meerschaert, Mark M.","first_name":"Mark M.","last_name":"Meerschaert"}],"title":"Space‐time fractional Dirichlet problems","year":"2018","doi":"10.1002/mana.201700111","language":[{"iso":"eng"}],"publication":"Mathematische Nachrichten","issue":"17-18","department":[{"_id":"555"}],"keyword":["General Mathematics"],"type":"journal_article","date_created":"2023-01-25T15:11:01Z"},{"doi":"10.1016/j.aim.2017.03.025","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2022-05-19T10:15:00Z","intvolume":"       313","title":"Wave front sets of reductive Lie group representations III","year":"2017","publication_identifier":{"issn":["0001-8708"]},"author":[{"first_name":"Benjamin","last_name":"Harris","full_name":"Harris, Benjamin"},{"id":"49178","orcid":"0000-0002-9648-6919","first_name":"Tobias","last_name":"Weich","full_name":"Weich, Tobias"}],"keyword":["General Mathematics"],"type":"journal_article","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"date_created":"2022-05-17T12:16:37Z","publication":"Advances in Mathematics","user_id":"49178","volume":313,"page":"176-236","_id":"31272","publisher":"Elsevier BV","status":"public","external_id":{"arxiv":["1503.08431"]},"citation":{"ieee":"B. Harris and T. Weich, “Wave front sets of reductive Lie group representations III,” <i>Advances in Mathematics</i>, vol. 313, pp. 176–236, 2017, doi: <a href=\"https://doi.org/10.1016/j.aim.2017.03.025\">10.1016/j.aim.2017.03.025</a>.","apa":"Harris, B., &#38; Weich, T. (2017). Wave front sets of reductive Lie group representations III. <i>Advances in Mathematics</i>, <i>313</i>, 176–236. <a href=\"https://doi.org/10.1016/j.aim.2017.03.025\">https://doi.org/10.1016/j.aim.2017.03.025</a>","short":"B. Harris, T. Weich, Advances in Mathematics 313 (2017) 176–236.","chicago":"Harris, Benjamin, and Tobias Weich. “Wave Front Sets of Reductive Lie Group Representations III.” <i>Advances in Mathematics</i> 313 (2017): 176–236. <a href=\"https://doi.org/10.1016/j.aim.2017.03.025\">https://doi.org/10.1016/j.aim.2017.03.025</a>.","mla":"Harris, Benjamin, and Tobias Weich. “Wave Front Sets of Reductive Lie Group Representations III.” <i>Advances in Mathematics</i>, vol. 313, Elsevier BV, 2017, pp. 176–236, doi:<a href=\"https://doi.org/10.1016/j.aim.2017.03.025\">10.1016/j.aim.2017.03.025</a>.","bibtex":"@article{Harris_Weich_2017, title={Wave front sets of reductive Lie group representations III}, volume={313}, DOI={<a href=\"https://doi.org/10.1016/j.aim.2017.03.025\">10.1016/j.aim.2017.03.025</a>}, journal={Advances in Mathematics}, publisher={Elsevier BV}, author={Harris, Benjamin and Weich, Tobias}, year={2017}, pages={176–236} }","ama":"Harris B, Weich T. Wave front sets of reductive Lie group representations III. <i>Advances in Mathematics</i>. 2017;313:176-236. doi:<a href=\"https://doi.org/10.1016/j.aim.2017.03.025\">10.1016/j.aim.2017.03.025</a>"}},{"intvolume":"       370","publication_status":"published","date_updated":"2024-02-19T06:18:21Z","publication_identifier":{"issn":["0025-5831","1432-1807"]},"author":[{"full_name":"Guillarmou, Colin","last_name":"Guillarmou","first_name":"Colin"},{"id":"220","full_name":"Hilgert, Joachim","first_name":"Joachim","last_name":"Hilgert"},{"id":"49178","full_name":"Weich, Tobias","last_name":"Weich","first_name":"Tobias","orcid":"0000-0002-9648-6919"}],"title":"Classical and quantum resonances for hyperbolic surfaces","year":"2017","doi":"10.1007/s00208-017-1576-5","language":[{"iso":"eng"}],"issue":"3-4","publication":"Mathematische Annalen","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"keyword":["General Mathematics"],"type":"journal_article","date_created":"2022-05-17T12:09:43Z","status":"public","volume":370,"user_id":"49063","publisher":"Springer Science and Business Media LLC","_id":"31267","page":"1231-1275","citation":{"bibtex":"@article{Guillarmou_Hilgert_Weich_2017, title={Classical and quantum resonances for hyperbolic surfaces}, volume={370}, DOI={<a href=\"https://doi.org/10.1007/s00208-017-1576-5\">10.1007/s00208-017-1576-5</a>}, number={3–4}, journal={Mathematische Annalen}, publisher={Springer Science and Business Media LLC}, author={Guillarmou, Colin and Hilgert, Joachim and Weich, Tobias}, year={2017}, pages={1231–1275} }","ama":"Guillarmou C, Hilgert J, Weich T. Classical and quantum resonances for hyperbolic surfaces. <i>Mathematische Annalen</i>. 2017;370(3-4):1231-1275. doi:<a href=\"https://doi.org/10.1007/s00208-017-1576-5\">10.1007/s00208-017-1576-5</a>","mla":"Guillarmou, Colin, et al. “Classical and Quantum Resonances for Hyperbolic Surfaces.” <i>Mathematische Annalen</i>, vol. 370, no. 3–4, Springer Science and Business Media LLC, 2017, pp. 1231–75, doi:<a href=\"https://doi.org/10.1007/s00208-017-1576-5\">10.1007/s00208-017-1576-5</a>.","chicago":"Guillarmou, Colin, Joachim Hilgert, and Tobias Weich. “Classical and Quantum Resonances for Hyperbolic Surfaces.” <i>Mathematische Annalen</i> 370, no. 3–4 (2017): 1231–75. <a href=\"https://doi.org/10.1007/s00208-017-1576-5\">https://doi.org/10.1007/s00208-017-1576-5</a>.","short":"C. Guillarmou, J. Hilgert, T. Weich, Mathematische Annalen 370 (2017) 1231–1275.","ieee":"C. Guillarmou, J. Hilgert, and T. Weich, “Classical and quantum resonances for hyperbolic surfaces,” <i>Mathematische Annalen</i>, vol. 370, no. 3–4, pp. 1231–1275, 2017, doi: <a href=\"https://doi.org/10.1007/s00208-017-1576-5\">10.1007/s00208-017-1576-5</a>.","apa":"Guillarmou, C., Hilgert, J., &#38; Weich, T. (2017). Classical and quantum resonances for hyperbolic surfaces. <i>Mathematische Annalen</i>, <i>370</i>(3–4), 1231–1275. <a href=\"https://doi.org/10.1007/s00208-017-1576-5\">https://doi.org/10.1007/s00208-017-1576-5</a>"},"external_id":{"arxiv":["1605.08801"]}},{"citation":{"mla":"Kovács, Balázs. “High-Order Evolving Surface Finite Element Method for Parabolic Problems on Evolving Surfaces.” <i>IMA Journal of Numerical Analysis</i>, vol. 38, no. 1, Oxford University Press (OUP), 2017, pp. 430–59, doi:<a href=\"https://doi.org/10.1093/imanum/drx013\">10.1093/imanum/drx013</a>.","bibtex":"@article{Kovács_2017, title={High-order evolving surface finite element method for parabolic problems on evolving surfaces}, volume={38}, DOI={<a href=\"https://doi.org/10.1093/imanum/drx013\">10.1093/imanum/drx013</a>}, number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Kovács, Balázs}, year={2017}, pages={430–459} }","ama":"Kovács B. High-order evolving surface finite element method for parabolic problems on evolving surfaces. <i>IMA Journal of Numerical Analysis</i>. 2017;38(1):430-459. doi:<a href=\"https://doi.org/10.1093/imanum/drx013\">10.1093/imanum/drx013</a>","ieee":"B. Kovács, “High-order evolving surface finite element method for parabolic problems on evolving surfaces,” <i>IMA Journal of Numerical Analysis</i>, vol. 38, no. 1, pp. 430–459, 2017, doi: <a href=\"https://doi.org/10.1093/imanum/drx013\">10.1093/imanum/drx013</a>.","apa":"Kovács, B. (2017). High-order evolving surface finite element method for parabolic problems on evolving surfaces. <i>IMA Journal of Numerical Analysis</i>, <i>38</i>(1), 430–459. <a href=\"https://doi.org/10.1093/imanum/drx013\">https://doi.org/10.1093/imanum/drx013</a>","chicago":"Kovács, Balázs. “High-Order Evolving Surface Finite Element Method for Parabolic Problems on Evolving Surfaces.” <i>IMA Journal of Numerical Analysis</i> 38, no. 1 (2017): 430–59. <a href=\"https://doi.org/10.1093/imanum/drx013\">https://doi.org/10.1093/imanum/drx013</a>.","short":"B. Kovács, IMA Journal of Numerical Analysis 38 (2017) 430–459."},"page":"430-459","_id":"45943","publisher":"Oxford University Press (OUP)","user_id":"100441","volume":38,"status":"public","date_created":"2023-07-10T11:39:23Z","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article","department":[{"_id":"841"}],"issue":"1","publication":"IMA Journal of Numerical Analysis","language":[{"iso":"eng"}],"doi":"10.1093/imanum/drx013","title":"High-order evolving surface finite element method for parabolic problems on evolving surfaces","year":"2017","author":[{"id":"100441","orcid":"0000-0001-9872-3474","last_name":"Kovács","first_name":"Balázs","full_name":"Kovács, Balázs"}],"publication_identifier":{"issn":["0272-4979","1464-3642"]},"date_updated":"2024-04-03T09:22:26Z","publication_status":"published","intvolume":"        38"},{"title":"Rational structures on automorphic representations","year":"2017","publication_identifier":{"issn":["0025-5831","1432-1807"]},"author":[{"full_name":"Januszewski, Fabian","first_name":"Fabian","last_name":"Januszewski","id":"81636"}],"date_updated":"2024-04-03T17:12:59Z","publication_status":"published","intvolume":"       370","article_type":"original","language":[{"iso":"eng"}],"doi":"10.1007/s00208-017-1567-6","issue":"3-4","publication":"Mathematische Annalen","extern":"1","date_created":"2024-04-03T16:54:45Z","keyword":["General Mathematics"],"type":"journal_article","status":"public","page":"1805-1881","_id":"53189","publisher":"Springer Science and Business Media LLC","user_id":"81636","volume":370,"citation":{"chicago":"Januszewski, Fabian. “Rational Structures on Automorphic Representations.” <i>Mathematische Annalen</i> 370, no. 3–4 (2017): 1805–81. <a href=\"https://doi.org/10.1007/s00208-017-1567-6\">https://doi.org/10.1007/s00208-017-1567-6</a>.","short":"F. Januszewski, Mathematische Annalen 370 (2017) 1805–1881.","apa":"Januszewski, F. (2017). Rational structures on automorphic representations. <i>Mathematische Annalen</i>, <i>370</i>(3–4), 1805–1881. <a href=\"https://doi.org/10.1007/s00208-017-1567-6\">https://doi.org/10.1007/s00208-017-1567-6</a>","ieee":"F. Januszewski, “Rational structures on automorphic representations,” <i>Mathematische Annalen</i>, vol. 370, no. 3–4, pp. 1805–1881, 2017, doi: <a href=\"https://doi.org/10.1007/s00208-017-1567-6\">10.1007/s00208-017-1567-6</a>.","ama":"Januszewski F. Rational structures on automorphic representations. <i>Mathematische Annalen</i>. 2017;370(3-4):1805-1881. doi:<a href=\"https://doi.org/10.1007/s00208-017-1567-6\">10.1007/s00208-017-1567-6</a>","bibtex":"@article{Januszewski_2017, title={Rational structures on automorphic representations}, volume={370}, DOI={<a href=\"https://doi.org/10.1007/s00208-017-1567-6\">10.1007/s00208-017-1567-6</a>}, number={3–4}, journal={Mathematische Annalen}, publisher={Springer Science and Business Media LLC}, author={Januszewski, Fabian}, year={2017}, pages={1805–1881} }","mla":"Januszewski, Fabian. “Rational Structures on Automorphic Representations.” <i>Mathematische Annalen</i>, vol. 370, no. 3–4, Springer Science and Business Media LLC, 2017, pp. 1805–81, doi:<a href=\"https://doi.org/10.1007/s00208-017-1567-6\">10.1007/s00208-017-1567-6</a>."}},{"doi":"10.1007/s10763-017-9857-8","language":[{"iso":"eng"}],"intvolume":"        17","publication_status":"published","date_updated":"2024-04-18T09:04:07Z","author":[{"full_name":"Schüler-Meyer, Alexander","last_name":"Schüler-Meyer","first_name":"Alexander"},{"full_name":"Prediger, Susanne","first_name":"Susanne","last_name":"Prediger"},{"last_name":"Kuzu","first_name":"Taha","full_name":"Kuzu, Taha"},{"id":"85190","full_name":"Wessel, Lena","first_name":"Lena","last_name":"Wessel"},{"full_name":"Redder, Angelika","first_name":"Angelika","last_name":"Redder"}],"publication_identifier":{"issn":["1571-0068","1573-1774"]},"year":"2017","title":"Is Formal Language Proficiency in the Home Language Required to Profit from a Bilingual Teaching Intervention in Mathematics? A Mixed Methods Study on Fostering Multilingual Students’ Conceptual Understanding","department":[{"_id":"643"}],"keyword":["General Mathematics","Education"],"type":"journal_article","date_created":"2023-10-19T09:31:20Z","publication":"International Journal of Science and Mathematics Education","issue":"2","volume":17,"user_id":"37888","publisher":"Springer Science and Business Media LLC","_id":"48323","page":"317-339","status":"public","citation":{"bibtex":"@article{Schüler-Meyer_Prediger_Kuzu_Wessel_Redder_2017, title={Is Formal Language Proficiency in the Home Language Required to Profit from a Bilingual Teaching Intervention in Mathematics? A Mixed Methods Study on Fostering Multilingual Students’ Conceptual Understanding}, volume={17}, DOI={<a href=\"https://doi.org/10.1007/s10763-017-9857-8\">10.1007/s10763-017-9857-8</a>}, number={2}, journal={International Journal of Science and Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Schüler-Meyer, Alexander and Prediger, Susanne and Kuzu, Taha and Wessel, Lena and Redder, Angelika}, year={2017}, pages={317–339} }","ama":"Schüler-Meyer A, Prediger S, Kuzu T, Wessel L, Redder A. Is Formal Language Proficiency in the Home Language Required to Profit from a Bilingual Teaching Intervention in Mathematics? A Mixed Methods Study on Fostering Multilingual Students’ Conceptual Understanding. <i>International Journal of Science and Mathematics Education</i>. 2017;17(2):317-339. doi:<a href=\"https://doi.org/10.1007/s10763-017-9857-8\">10.1007/s10763-017-9857-8</a>","mla":"Schüler-Meyer, Alexander, et al. “Is Formal Language Proficiency in the Home Language Required to Profit from a Bilingual Teaching Intervention in Mathematics? A Mixed Methods Study on Fostering Multilingual Students’ Conceptual Understanding.” <i>International Journal of Science and Mathematics Education</i>, vol. 17, no. 2, Springer Science and Business Media LLC, 2017, pp. 317–39, doi:<a href=\"https://doi.org/10.1007/s10763-017-9857-8\">10.1007/s10763-017-9857-8</a>.","short":"A. Schüler-Meyer, S. Prediger, T. Kuzu, L. Wessel, A. Redder, International Journal of Science and Mathematics Education 17 (2017) 317–339.","chicago":"Schüler-Meyer, Alexander, Susanne Prediger, Taha Kuzu, Lena Wessel, and Angelika Redder. “Is Formal Language Proficiency in the Home Language Required to Profit from a Bilingual Teaching Intervention in Mathematics? A Mixed Methods Study on Fostering Multilingual Students’ Conceptual Understanding.” <i>International Journal of Science and Mathematics Education</i> 17, no. 2 (2017): 317–39. <a href=\"https://doi.org/10.1007/s10763-017-9857-8\">https://doi.org/10.1007/s10763-017-9857-8</a>.","ieee":"A. Schüler-Meyer, S. Prediger, T. Kuzu, L. Wessel, and A. Redder, “Is Formal Language Proficiency in the Home Language Required to Profit from a Bilingual Teaching Intervention in Mathematics? A Mixed Methods Study on Fostering Multilingual Students’ Conceptual Understanding,” <i>International Journal of Science and Mathematics Education</i>, vol. 17, no. 2, pp. 317–339, 2017, doi: <a href=\"https://doi.org/10.1007/s10763-017-9857-8\">10.1007/s10763-017-9857-8</a>.","apa":"Schüler-Meyer, A., Prediger, S., Kuzu, T., Wessel, L., &#38; Redder, A. (2017). Is Formal Language Proficiency in the Home Language Required to Profit from a Bilingual Teaching Intervention in Mathematics? A Mixed Methods Study on Fostering Multilingual Students’ Conceptual Understanding. <i>International Journal of Science and Mathematics Education</i>, <i>17</i>(2), 317–339. <a href=\"https://doi.org/10.1007/s10763-017-9857-8\">https://doi.org/10.1007/s10763-017-9857-8</a>"}},{"citation":{"ieee":"R. Lauterbach and S. Schwenker, “Equivariant bifurcations in four-dimensional fixed point spaces,” <i>Dynamical Systems</i>, vol. 32, no. 1, pp. 117–147, 2016, doi: <a href=\"https://doi.org/10.1080/14689367.2016.1219696\">10.1080/14689367.2016.1219696</a>.","apa":"Lauterbach, R., &#38; Schwenker, S. (2016). Equivariant bifurcations in four-dimensional fixed point spaces. <i>Dynamical Systems</i>, <i>32</i>(1), 117–147. <a href=\"https://doi.org/10.1080/14689367.2016.1219696\">https://doi.org/10.1080/14689367.2016.1219696</a>","short":"R. Lauterbach, S. Schwenker, Dynamical Systems 32 (2016) 117–147.","chicago":"Lauterbach, Reiner, and Sören Schwenker. “Equivariant Bifurcations in Four-Dimensional Fixed Point Spaces.” <i>Dynamical Systems</i> 32, no. 1 (2016): 117–47. <a href=\"https://doi.org/10.1080/14689367.2016.1219696\">https://doi.org/10.1080/14689367.2016.1219696</a>.","mla":"Lauterbach, Reiner, and Sören Schwenker. “Equivariant Bifurcations in Four-Dimensional Fixed Point Spaces.” <i>Dynamical Systems</i>, vol. 32, no. 1, Informa UK Limited, 2016, pp. 117–47, doi:<a href=\"https://doi.org/10.1080/14689367.2016.1219696\">10.1080/14689367.2016.1219696</a>.","bibtex":"@article{Lauterbach_Schwenker_2016, title={Equivariant bifurcations in four-dimensional fixed point spaces}, volume={32}, DOI={<a href=\"https://doi.org/10.1080/14689367.2016.1219696\">10.1080/14689367.2016.1219696</a>}, number={1}, journal={Dynamical Systems}, publisher={Informa UK Limited}, author={Lauterbach, Reiner and Schwenker, Sören}, year={2016}, pages={117–147} }","ama":"Lauterbach R, Schwenker S. Equivariant bifurcations in four-dimensional fixed point spaces. <i>Dynamical Systems</i>. 2016;32(1):117-147. doi:<a href=\"https://doi.org/10.1080/14689367.2016.1219696\">10.1080/14689367.2016.1219696</a>"},"external_id":{"arxiv":["1511.00545"]},"status":"public","publisher":"Informa UK Limited","_id":"33260","page":"117-147","volume":32,"user_id":"97359","issue":"1","publication":"Dynamical Systems","extern":"1","abstract":[{"lang":"eng","text":"In this paper we continue the study of group representations which are counterexamples to the Ize conjecture. As in previous papers we find new infinite series of finite groups leading to such counterexamples. These new series are quite different from the previous ones, for example the group orders do not form an arithmetic progression. However, as before we find Lie groups which contain all these groups. This additional structure was observed, but not used in the previous studies of this problem. Here we also investigate the related bifurcations. To a large extent, these are closely related to the presence of mentioned compact Lie group containing the finite groups. This might give a tool to study the bifurcations related to all low dimensional counterexamples of the Ize conjecture. It also gives an indication of where we can expect to find examples where the bifurcation behaviour is different from what we have seen in the known examples."}],"date_created":"2022-09-06T11:22:12Z","type":"journal_article","keyword":["Computer Science Applications","General Mathematics"],"author":[{"full_name":"Lauterbach, Reiner","first_name":"Reiner","last_name":"Lauterbach"},{"id":"97359","full_name":"Schwenker, Sören","orcid":"0000-0002-8054-2058","first_name":"Sören","last_name":"Schwenker"}],"publication_identifier":{"issn":["1468-9367","1468-9375"]},"title":"Equivariant bifurcations in four-dimensional fixed point spaces","year":"2016","intvolume":"        32","publication_status":"published","date_updated":"2022-09-07T08:33:36Z","language":[{"iso":"eng"}],"doi":"10.1080/14689367.2016.1219696"},{"publication_status":"published","date_updated":"2024-04-03T09:22:19Z","intvolume":"        38","year":"2016","title":"Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces","publication_identifier":{"issn":["0272-4979","1464-3642"]},"author":[{"id":"100441","full_name":"Kovács, Balázs","first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474"},{"last_name":"Power Guerra","first_name":"Christian Andreas","full_name":"Power Guerra, Christian Andreas"}],"doi":"10.1093/imanum/drw074","language":[{"iso":"eng"}],"publication":"IMA Journal of Numerical Analysis","issue":"1","type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"department":[{"_id":"841"}],"date_created":"2023-07-10T11:39:39Z","status":"public","user_id":"100441","volume":38,"page":"460-494","_id":"45944","publisher":"Oxford University Press (OUP)","citation":{"bibtex":"@article{Kovács_Power Guerra_2016, title={Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces}, volume={38}, DOI={<a href=\"https://doi.org/10.1093/imanum/drw074\">10.1093/imanum/drw074</a>}, number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Kovács, Balázs and Power Guerra, Christian Andreas}, year={2016}, pages={460–494} }","ama":"Kovács B, Power Guerra CA. Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces. <i>IMA Journal of Numerical Analysis</i>. 2016;38(1):460-494. doi:<a href=\"https://doi.org/10.1093/imanum/drw074\">10.1093/imanum/drw074</a>","mla":"Kovács, Balázs, and Christian Andreas Power Guerra. “Higher Order Time Discretizations with ALE Finite Elements for Parabolic Problems on Evolving Surfaces.” <i>IMA Journal of Numerical Analysis</i>, vol. 38, no. 1, Oxford University Press (OUP), 2016, pp. 460–94, doi:<a href=\"https://doi.org/10.1093/imanum/drw074\">10.1093/imanum/drw074</a>.","chicago":"Kovács, Balázs, and Christian Andreas Power Guerra. “Higher Order Time Discretizations with ALE Finite Elements for Parabolic Problems on Evolving Surfaces.” <i>IMA Journal of Numerical Analysis</i> 38, no. 1 (2016): 460–94. <a href=\"https://doi.org/10.1093/imanum/drw074\">https://doi.org/10.1093/imanum/drw074</a>.","short":"B. Kovács, C.A. Power Guerra, IMA Journal of Numerical Analysis 38 (2016) 460–494.","ieee":"B. Kovács and C. A. Power Guerra, “Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces,” <i>IMA Journal of Numerical Analysis</i>, vol. 38, no. 1, pp. 460–494, 2016, doi: <a href=\"https://doi.org/10.1093/imanum/drw074\">10.1093/imanum/drw074</a>.","apa":"Kovács, B., &#38; Power Guerra, C. A. (2016). Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces. <i>IMA Journal of Numerical Analysis</i>, <i>38</i>(1), 460–494. <a href=\"https://doi.org/10.1093/imanum/drw074\">https://doi.org/10.1093/imanum/drw074</a>"}},{"citation":{"bibtex":"@article{Kovács_Lubich_2016, title={Numerical analysis of parabolic problems with dynamic boundary conditions}, volume={37}, DOI={<a href=\"https://doi.org/10.1093/imanum/drw015\">10.1093/imanum/drw015</a>}, number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Kovács, Balázs and Lubich, Christian}, year={2016}, pages={1–39} }","ama":"Kovács B, Lubich C. Numerical analysis of parabolic problems with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>. 2016;37(1):1-39. doi:<a href=\"https://doi.org/10.1093/imanum/drw015\">10.1093/imanum/drw015</a>","mla":"Kovács, Balázs, and Christian Lubich. “Numerical Analysis of Parabolic Problems with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>, vol. 37, no. 1, Oxford University Press (OUP), 2016, pp. 1–39, doi:<a href=\"https://doi.org/10.1093/imanum/drw015\">10.1093/imanum/drw015</a>.","chicago":"Kovács, Balázs, and Christian Lubich. “Numerical Analysis of Parabolic Problems with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i> 37, no. 1 (2016): 1–39. <a href=\"https://doi.org/10.1093/imanum/drw015\">https://doi.org/10.1093/imanum/drw015</a>.","short":"B. Kovács, C. Lubich, IMA Journal of Numerical Analysis 37 (2016) 1–39.","ieee":"B. Kovács and C. Lubich, “Numerical analysis of parabolic problems with dynamic boundary conditions,” <i>IMA Journal of Numerical Analysis</i>, vol. 37, no. 1, pp. 1–39, 2016, doi: <a href=\"https://doi.org/10.1093/imanum/drw015\">10.1093/imanum/drw015</a>.","apa":"Kovács, B., &#38; Lubich, C. (2016). Numerical analysis of parabolic problems with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>, <i>37</i>(1), 1–39. <a href=\"https://doi.org/10.1093/imanum/drw015\">https://doi.org/10.1093/imanum/drw015</a>"},"user_id":"100441","volume":37,"page":"1-39","_id":"45937","publisher":"Oxford University Press (OUP)","status":"public","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article","department":[{"_id":"841"}],"date_created":"2023-07-10T11:35:53Z","issue":"1","publication":"IMA Journal of Numerical Analysis","doi":"10.1093/imanum/drw015","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2024-04-03T09:23:16Z","intvolume":"        37","year":"2016","title":"Numerical analysis of parabolic problems with dynamic boundary conditions","author":[{"id":"100441","orcid":"0000-0001-9872-3474","last_name":"Kovács","first_name":"Balázs","full_name":"Kovács, Balázs"},{"full_name":"Lubich, Christian","last_name":"Lubich","first_name":"Christian"}],"publication_identifier":{"issn":["0272-4979","1464-3642"]}},{"date_updated":"2024-04-03T17:18:24Z","publication_status":"published","intvolume":"        40","article_type":"original","title":"p-adic L-functions for Rankin–Selberg convolutions over number fields","year":"2016","publication_identifier":{"issn":["2195-4755","2195-4763"]},"author":[{"id":"81636","first_name":"Fabian","last_name":"Januszewski","full_name":"Januszewski, Fabian"}],"doi":"10.1007/s40316-016-0061-y","language":[{"iso":"eng"}],"extern":"1","publication":"Annales mathématiques du Québec; Special Issue in Honor of Glenn Stevens","issue":"2","type":"journal_article","keyword":["General Mathematics"],"date_created":"2024-04-03T16:54:10Z","status":"public","user_id":"81636","volume":40,"page":"453-489","_id":"53188","publisher":"Springer Science and Business Media LLC","citation":{"mla":"Januszewski, Fabian. “P-Adic L-Functions for Rankin–Selberg Convolutions over Number Fields.” <i>Annales Mathématiques Du Québec; Special Issue in Honor of Glenn Stevens</i>, vol. 40, no. 2, Springer Science and Business Media LLC, 2016, pp. 453–89, doi:<a href=\"https://doi.org/10.1007/s40316-016-0061-y\">10.1007/s40316-016-0061-y</a>.","ama":"Januszewski F. p-adic L-functions for Rankin–Selberg convolutions over number fields. <i>Annales mathématiques du Québec; Special Issue in Honor of Glenn Stevens</i>. 2016;40(2):453-489. doi:<a href=\"https://doi.org/10.1007/s40316-016-0061-y\">10.1007/s40316-016-0061-y</a>","bibtex":"@article{Januszewski_2016, title={p-adic L-functions for Rankin–Selberg convolutions over number fields}, volume={40}, DOI={<a href=\"https://doi.org/10.1007/s40316-016-0061-y\">10.1007/s40316-016-0061-y</a>}, number={2}, journal={Annales mathématiques du Québec; Special Issue in Honor of Glenn Stevens}, publisher={Springer Science and Business Media LLC}, author={Januszewski, Fabian}, year={2016}, pages={453–489} }","apa":"Januszewski, F. (2016). p-adic L-functions for Rankin–Selberg convolutions over number fields. <i>Annales Mathématiques Du Québec; Special Issue in Honor of Glenn Stevens</i>, <i>40</i>(2), 453–489. <a href=\"https://doi.org/10.1007/s40316-016-0061-y\">https://doi.org/10.1007/s40316-016-0061-y</a>","ieee":"F. Januszewski, “p-adic L-functions for Rankin–Selberg convolutions over number fields,” <i>Annales mathématiques du Québec; Special Issue in Honor of Glenn Stevens</i>, vol. 40, no. 2, pp. 453–489, 2016, doi: <a href=\"https://doi.org/10.1007/s40316-016-0061-y\">10.1007/s40316-016-0061-y</a>.","chicago":"Januszewski, Fabian. “P-Adic L-Functions for Rankin–Selberg Convolutions over Number Fields.” <i>Annales Mathématiques Du Québec; Special Issue in Honor of Glenn Stevens</i> 40, no. 2 (2016): 453–89. <a href=\"https://doi.org/10.1007/s40316-016-0061-y\">https://doi.org/10.1007/s40316-016-0061-y</a>.","short":"F. Januszewski, Annales Mathématiques Du Québec; Special Issue in Honor of Glenn Stevens 40 (2016) 453–489."}},{"citation":{"chicago":"Bañuelos, Rodrigo, Krzysztof Bogdan, and Tomasz Luks. “Hardy–Stein Identities and Square Functions for Semigroups.” <i>Journal of the London Mathematical Society</i> 94, no. 2 (2016): 462–78. <a href=\"https://doi.org/10.1112/jlms/jdw042\">https://doi.org/10.1112/jlms/jdw042</a>.","short":"R. Bañuelos, K. Bogdan, T. Luks, Journal of the London Mathematical Society 94 (2016) 462–478.","ieee":"R. Bañuelos, K. Bogdan, and T. Luks, “Hardy–Stein identities and square functions for semigroups,” <i>Journal of the London Mathematical Society</i>, vol. 94, no. 2, pp. 462–478, 2016, doi: <a href=\"https://doi.org/10.1112/jlms/jdw042\">10.1112/jlms/jdw042</a>.","apa":"Bañuelos, R., Bogdan, K., &#38; Luks, T. (2016). Hardy–Stein identities and square functions for semigroups. <i>Journal of the London Mathematical Society</i>, <i>94</i>(2), 462–478. <a href=\"https://doi.org/10.1112/jlms/jdw042\">https://doi.org/10.1112/jlms/jdw042</a>","bibtex":"@article{Bañuelos_Bogdan_Luks_2016, title={Hardy–Stein identities and square functions for semigroups}, volume={94}, DOI={<a href=\"https://doi.org/10.1112/jlms/jdw042\">10.1112/jlms/jdw042</a>}, number={2}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Bañuelos, Rodrigo and Bogdan, Krzysztof and Luks, Tomasz}, year={2016}, pages={462–478} }","ama":"Bañuelos R, Bogdan K, Luks T. Hardy–Stein identities and square functions for semigroups. <i>Journal of the London Mathematical Society</i>. 2016;94(2):462-478. doi:<a href=\"https://doi.org/10.1112/jlms/jdw042\">10.1112/jlms/jdw042</a>","mla":"Bañuelos, Rodrigo, et al. “Hardy–Stein Identities and Square Functions for Semigroups.” <i>Journal of the London Mathematical Society</i>, vol. 94, no. 2, Wiley, 2016, pp. 462–78, doi:<a href=\"https://doi.org/10.1112/jlms/jdw042\">10.1112/jlms/jdw042</a>."},"user_id":"58312","volume":94,"page":"462-478","publisher":"Wiley","_id":"40066","status":"public","keyword":["General Mathematics"],"type":"journal_article","department":[{"_id":"555"}],"date_created":"2023-01-25T15:43:14Z","extern":"1","publication":"Journal of the London Mathematical Society","issue":"2","doi":"10.1112/jlms/jdw042","language":[{"iso":"eng"}],"date_updated":"2023-01-26T17:20:19Z","publication_status":"published","intvolume":"        94","year":"2016","title":"Hardy–Stein identities and square functions for semigroups","publication_identifier":{"issn":["0024-6107","1469-7750"]},"author":[{"full_name":"Bañuelos, Rodrigo","first_name":"Rodrigo","last_name":"Bañuelos"},{"full_name":"Bogdan, Krzysztof","first_name":"Krzysztof","last_name":"Bogdan"},{"id":"58312","first_name":"Tomasz","last_name":"Luks","full_name":"Luks, Tomasz"}]},{"publication_status":"published","date_updated":"2022-05-19T10:15:54Z","intvolume":"        37","year":"2015","title":"Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps","author":[{"full_name":"ARNOLDI, JEAN FRANCOIS","last_name":"ARNOLDI","first_name":"JEAN FRANCOIS"},{"full_name":"FAURE, FRÉDÉRIC","first_name":"FRÉDÉRIC","last_name":"FAURE"},{"id":"49178","first_name":"Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","full_name":"Weich, Tobias"}],"publication_identifier":{"issn":["0143-3857","1469-4417"]},"doi":"10.1017/etds.2015.34","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"<jats:p>We consider a simple model of an open partially expanding map. Its trapped set <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0143385715000346_inline1\" /><jats:tex-math>${\\mathcal{K}}$</jats:tex-math></jats:alternatives></jats:inline-formula> in phase space is a fractal set. We first show that there is a well-defined discrete spectrum of Ruelle resonances which describes the asymptotic of correlation functions for large time and which is parametrized by the Fourier component <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0143385715000346_inline2\" /><jats:tex-math>$\\unicode[STIX]{x1D708}$</jats:tex-math></jats:alternatives></jats:inline-formula> in the neutral direction of the dynamics. We introduce a specific hypothesis on the dynamics that we call ‘minimal captivity’. This hypothesis is stable under perturbations and means that the dynamics is univalued in a neighborhood of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0143385715000346_inline3\" /><jats:tex-math>${\\mathcal{K}}$</jats:tex-math></jats:alternatives></jats:inline-formula>. Under this hypothesis we show the existence of an asymptotic spectral gap and a fractal Weyl law for the upper bound of density of Ruelle resonances in the semiclassical limit <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0143385715000346_inline4\" /><jats:tex-math>$\\unicode[STIX]{x1D708}\\rightarrow \\infty$</jats:tex-math></jats:alternatives></jats:inline-formula>. Some numerical computations with the truncated Gauss map and Bowen–Series maps illustrate these results.</jats:p>"}],"issue":"1","publication":"Ergodic Theory and Dynamical Systems","keyword":["Applied Mathematics","General Mathematics"],"type":"journal_article","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"date_created":"2022-05-17T12:55:26Z","status":"public","user_id":"49178","volume":37,"page":"1-58","publisher":"Cambridge University Press (CUP)","_id":"31291","citation":{"chicago":"ARNOLDI, JEAN FRANCOIS, FRÉDÉRIC FAURE, and Tobias Weich. “Asymptotic Spectral Gap and Weyl Law for Ruelle Resonances of Open Partially Expanding Maps.” <i>Ergodic Theory and Dynamical Systems</i> 37, no. 1 (2015): 1–58. <a href=\"https://doi.org/10.1017/etds.2015.34\">https://doi.org/10.1017/etds.2015.34</a>.","short":"J.F. ARNOLDI, F. FAURE, T. Weich, Ergodic Theory and Dynamical Systems 37 (2015) 1–58.","apa":"ARNOLDI, J. F., FAURE, F., &#38; Weich, T. (2015). Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps. <i>Ergodic Theory and Dynamical Systems</i>, <i>37</i>(1), 1–58. <a href=\"https://doi.org/10.1017/etds.2015.34\">https://doi.org/10.1017/etds.2015.34</a>","ieee":"J. F. ARNOLDI, F. FAURE, and T. Weich, “Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps,” <i>Ergodic Theory and Dynamical Systems</i>, vol. 37, no. 1, pp. 1–58, 2015, doi: <a href=\"https://doi.org/10.1017/etds.2015.34\">10.1017/etds.2015.34</a>.","ama":"ARNOLDI JF, FAURE F, Weich T. Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps. <i>Ergodic Theory and Dynamical Systems</i>. 2015;37(1):1-58. doi:<a href=\"https://doi.org/10.1017/etds.2015.34\">10.1017/etds.2015.34</a>","bibtex":"@article{ARNOLDI_FAURE_Weich_2015, title={Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps}, volume={37}, DOI={<a href=\"https://doi.org/10.1017/etds.2015.34\">10.1017/etds.2015.34</a>}, number={1}, journal={Ergodic Theory and Dynamical Systems}, publisher={Cambridge University Press (CUP)}, author={ARNOLDI, JEAN FRANCOIS and FAURE, FRÉDÉRIC and Weich, Tobias}, year={2015}, pages={1–58} }","mla":"ARNOLDI, JEAN FRANCOIS, et al. “Asymptotic Spectral Gap and Weyl Law for Ruelle Resonances of Open Partially Expanding Maps.” <i>Ergodic Theory and Dynamical Systems</i>, vol. 37, no. 1, Cambridge University Press (CUP), 2015, pp. 1–58, doi:<a href=\"https://doi.org/10.1017/etds.2015.34\">10.1017/etds.2015.34</a>."},"external_id":{"arxiv":["1302.3087"]}},{"citation":{"chicago":"Januszewski, Fabian. “On P-Adic L-Functions for GL(n) × GL (n-1) over Totally Real Fields.” <i>International Mathematics Research Notices</i> 2015, no. 17 (2014): 7884–7949. <a href=\"https://doi.org/10.1093/imrn/rnu181\">https://doi.org/10.1093/imrn/rnu181</a>.","short":"F. Januszewski, International Mathematics Research Notices 2015 (2014) 7884–7949.","ieee":"F. Januszewski, “On p-adic L-functions for GL(n) × GL (n-1) over totally real fields,” <i>International Mathematics Research Notices</i>, vol. 2015, no. 17, pp. 7884–7949, 2014, doi: <a href=\"https://doi.org/10.1093/imrn/rnu181\">10.1093/imrn/rnu181</a>.","apa":"Januszewski, F. (2014). On p-adic L-functions for GL(n) × GL (n-1) over totally real fields. <i>International Mathematics Research Notices</i>, <i>2015</i>(17), 7884–7949. <a href=\"https://doi.org/10.1093/imrn/rnu181\">https://doi.org/10.1093/imrn/rnu181</a>","bibtex":"@article{Januszewski_2014, title={On p-adic L-functions for GL(n) × GL (n-1) over totally real fields}, volume={2015}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnu181\">10.1093/imrn/rnu181</a>}, number={17}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Januszewski, Fabian}, year={2014}, pages={7884–7949} }","ama":"Januszewski F. On p-adic L-functions for GL(n) × GL (n-1) over totally real fields. <i>International Mathematics Research Notices</i>. 2014;2015(17):7884-7949. doi:<a href=\"https://doi.org/10.1093/imrn/rnu181\">10.1093/imrn/rnu181</a>","mla":"Januszewski, Fabian. “On P-Adic L-Functions for GL(n) × GL (n-1) over Totally Real Fields.” <i>International Mathematics Research Notices</i>, vol. 2015, no. 17, Oxford University Press (OUP), 2014, pp. 7884–949, doi:<a href=\"https://doi.org/10.1093/imrn/rnu181\">10.1093/imrn/rnu181</a>."},"status":"public","page":"7884-7949","publisher":"Oxford University Press (OUP)","_id":"53185","user_id":"81636","volume":2015,"issue":"17","publication":"International Mathematics Research Notices","extern":"1","date_created":"2024-04-03T16:48:18Z","keyword":["General Mathematics"],"type":"journal_article","year":"2014","title":"On p-adic L-functions for GL(n) × GL (n-1) over totally real fields","publication_identifier":{"issn":["1073-7928","1687-0247"]},"author":[{"id":"81636","last_name":"Januszewski","first_name":"Fabian","full_name":"Januszewski, Fabian"}],"publication_status":"published","date_updated":"2024-04-03T17:12:38Z","article_type":"original","intvolume":"      2015","language":[{"iso":"eng"}],"doi":"10.1093/imrn/rnu181"},{"publication":"Journal of Approximation Theory","date_created":"2023-01-20T09:30:22Z","department":[{"_id":"555"}],"type":"journal_article","keyword":["Applied Mathematics","General Mathematics","Numerical Analysis","Analysis"],"author":[{"full_name":"Rösler, Margit","first_name":"Margit","last_name":"Rösler","id":"37390"},{"first_name":"Heiko","last_name":"Remling","full_name":"Remling, Heiko"}],"publication_identifier":{"issn":["0021-9045"]},"year":"2014","title":"Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians","intvolume":"       197","publication_status":"published","date_updated":"2023-01-24T22:15:33Z","language":[{"iso":"eng"}],"doi":"10.1016/j.jat.2014.07.005","citation":{"short":"M. Rösler, H. Remling, Journal of Approximation Theory 197 (2014) 30–48.","chicago":"Rösler, Margit, and Heiko Remling. “Convolution Algebras for Heckman–Opdam Polynomials Derived from Compact Grassmannians.” <i>Journal of Approximation Theory</i> 197 (2014): 30–48. <a href=\"https://doi.org/10.1016/j.jat.2014.07.005\">https://doi.org/10.1016/j.jat.2014.07.005</a>.","apa":"Rösler, M., &#38; Remling, H. (2014). Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians. <i>Journal of Approximation Theory</i>, <i>197</i>, 30–48. <a href=\"https://doi.org/10.1016/j.jat.2014.07.005\">https://doi.org/10.1016/j.jat.2014.07.005</a>","ieee":"M. Rösler and H. Remling, “Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians,” <i>Journal of Approximation Theory</i>, vol. 197, pp. 30–48, 2014, doi: <a href=\"https://doi.org/10.1016/j.jat.2014.07.005\">10.1016/j.jat.2014.07.005</a>.","ama":"Rösler M, Remling H. Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians. <i>Journal of Approximation Theory</i>. 2014;197:30-48. doi:<a href=\"https://doi.org/10.1016/j.jat.2014.07.005\">10.1016/j.jat.2014.07.005</a>","bibtex":"@article{Rösler_Remling_2014, title={Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians}, volume={197}, DOI={<a href=\"https://doi.org/10.1016/j.jat.2014.07.005\">10.1016/j.jat.2014.07.005</a>}, journal={Journal of Approximation Theory}, publisher={Elsevier BV}, author={Rösler, Margit and Remling, Heiko}, year={2014}, pages={30–48} }","mla":"Rösler, Margit, and Heiko Remling. “Convolution Algebras for Heckman–Opdam Polynomials Derived from Compact Grassmannians.” <i>Journal of Approximation Theory</i>, vol. 197, Elsevier BV, 2014, pp. 30–48, doi:<a href=\"https://doi.org/10.1016/j.jat.2014.07.005\">10.1016/j.jat.2014.07.005</a>."},"status":"public","_id":"37667","publisher":"Elsevier BV","page":"30-48","volume":197,"user_id":"93826"},{"status":"public","user_id":"93826","volume":17,"page":"141-158","publisher":"Wiley","_id":"34845","citation":{"ama":"Fieker C, Klüners J. Computation of Galois groups of rational polynomials. <i>LMS Journal of Computation and Mathematics</i>. 2014;17(1):141-158. doi:<a href=\"https://doi.org/10.1112/s1461157013000302\">10.1112/s1461157013000302</a>","bibtex":"@article{Fieker_Klüners_2014, title={Computation of Galois groups of rational polynomials}, volume={17}, DOI={<a href=\"https://doi.org/10.1112/s1461157013000302\">10.1112/s1461157013000302</a>}, number={1}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Fieker, Claus and Klüners, Jürgen}, year={2014}, pages={141–158} }","mla":"Fieker, Claus, and Jürgen Klüners. “Computation of Galois Groups of Rational Polynomials.” <i>LMS Journal of Computation and Mathematics</i>, vol. 17, no. 1, Wiley, 2014, pp. 141–58, doi:<a href=\"https://doi.org/10.1112/s1461157013000302\">10.1112/s1461157013000302</a>.","short":"C. Fieker, J. Klüners, LMS Journal of Computation and Mathematics 17 (2014) 141–158.","chicago":"Fieker, Claus, and Jürgen Klüners. “Computation of Galois Groups of Rational Polynomials.” <i>LMS Journal of Computation and Mathematics</i> 17, no. 1 (2014): 141–58. <a href=\"https://doi.org/10.1112/s1461157013000302\">https://doi.org/10.1112/s1461157013000302</a>.","apa":"Fieker, C., &#38; Klüners, J. (2014). Computation of Galois groups of rational polynomials. <i>LMS Journal of Computation and Mathematics</i>, <i>17</i>(1), 141–158. <a href=\"https://doi.org/10.1112/s1461157013000302\">https://doi.org/10.1112/s1461157013000302</a>","ieee":"C. Fieker and J. Klüners, “Computation of Galois groups of rational polynomials,” <i>LMS Journal of Computation and Mathematics</i>, vol. 17, no. 1, pp. 141–158, 2014, doi: <a href=\"https://doi.org/10.1112/s1461157013000302\">10.1112/s1461157013000302</a>."},"external_id":{"arxiv":["1211.3588"]},"date_updated":"2023-03-06T09:43:56Z","publication_status":"published","intvolume":"        17","title":"Computation of Galois groups of rational polynomials","year":"2014","author":[{"full_name":"Fieker, Claus","last_name":"Fieker","first_name":"Claus"},{"id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen"}],"publication_identifier":{"issn":["1461-1570"]},"doi":"10.1112/s1461157013000302","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Computational Galois theory, in particular the problem of computing the Galois group of a given polynomial, is a very old problem. Currently, the best algorithmic solution is Stauduhar’s method. Computationally, one of the key challenges in the application of Stauduhar’s method is to find, for a given pair of groups H<G, a G-relative H-invariant, that is a multivariate polynomial F that is H-invariant, but not G-invariant. While generic, theoretical methods are known to find such F, in general they yield impractical answers. We give a general method for computing invariants of large degree which improves on previous known methods, as well as various special invariants that are derived from the structure of the groups. We then apply our new invariants to the task of computing the Galois groups of polynomials over the rational numbers, resulting in the first practical degree independent algorithm."}],"publication":"LMS Journal of Computation and Mathematics","issue":"1","keyword":["Computational Theory and Mathematics","General Mathematics"],"type":"journal_article","department":[{"_id":"102"}],"date_created":"2022-12-22T10:53:44Z"},{"_id":"42801","publisher":"Cambridge University Press (CUP)","page":"173-180","volume":57,"user_id":"93826","status":"public","citation":{"mla":"Kirschmer, Markus, and CHARLES LEEDHAM-GREEN. “Computing with Subgroups of the Modular Group .” <i>Glasgow Mathematical Journal</i>, vol. 57, no. 1, Cambridge University Press (CUP), 2014, pp. 173–80, doi:<a href=\"https://doi.org/10.1017/s0017089514000202\">10.1017/s0017089514000202</a>.","ama":"Kirschmer M, LEEDHAM-GREEN C. Computing with subgroups of the modular group . <i>Glasgow Mathematical Journal</i>. 2014;57(1):173-180. doi:<a href=\"https://doi.org/10.1017/s0017089514000202\">10.1017/s0017089514000202</a>","bibtex":"@article{Kirschmer_LEEDHAM-GREEN_2014, title={Computing with subgroups of the modular group }, volume={57}, DOI={<a href=\"https://doi.org/10.1017/s0017089514000202\">10.1017/s0017089514000202</a>}, number={1}, journal={Glasgow Mathematical Journal}, publisher={Cambridge University Press (CUP)}, author={Kirschmer, Markus and LEEDHAM-GREEN, CHARLES}, year={2014}, pages={173–180} }","apa":"Kirschmer, M., &#38; LEEDHAM-GREEN, C. (2014). Computing with subgroups of the modular group . <i>Glasgow Mathematical Journal</i>, <i>57</i>(1), 173–180. <a href=\"https://doi.org/10.1017/s0017089514000202\">https://doi.org/10.1017/s0017089514000202</a>","ieee":"M. Kirschmer and C. LEEDHAM-GREEN, “Computing with subgroups of the modular group ,” <i>Glasgow Mathematical Journal</i>, vol. 57, no. 1, pp. 173–180, 2014, doi: <a href=\"https://doi.org/10.1017/s0017089514000202\">10.1017/s0017089514000202</a>.","short":"M. Kirschmer, C. LEEDHAM-GREEN, Glasgow Mathematical Journal 57 (2014) 173–180.","chicago":"Kirschmer, Markus, and CHARLES LEEDHAM-GREEN. “Computing with Subgroups of the Modular Group .” <i>Glasgow Mathematical Journal</i> 57, no. 1 (2014): 173–80. <a href=\"https://doi.org/10.1017/s0017089514000202\">https://doi.org/10.1017/s0017089514000202</a>."},"language":[{"iso":"eng"}],"doi":"10.1017/s0017089514000202","author":[{"first_name":"Markus","last_name":"Kirschmer","full_name":"Kirschmer, Markus","id":"82258"},{"full_name":"LEEDHAM-GREEN, CHARLES","first_name":"CHARLES","last_name":"LEEDHAM-GREEN"}],"publication_identifier":{"issn":["0017-0895","1469-509X"]},"title":"Computing with subgroups of the modular group ","year":"2014","intvolume":"        57","publication_status":"published","date_updated":"2023-04-04T07:55:16Z","date_created":"2023-03-07T08:47:42Z","department":[{"_id":"102"}],"type":"journal_article","keyword":["General Mathematics"],"issue":"1","publication":"Glasgow Mathematical Journal","extern":"1","abstract":[{"lang":"eng","text":"We exhibit a practical algorithm for solving the constructive membership problem for discrete free subgroups of rank 2 in PSL₂(R) or SL₂(R). This algorithm, together with methods for checking whether a two-generator subgroup of PSL₂(R) or SL₂(R) is discrete and free, have been implemented in Magma for groups defined over real algebraic number fields."}]},{"doi":"10.1112/s1461157014000047","language":[{"iso":"eng"}],"intvolume":"        17","publication_status":"published","date_updated":"2023-04-04T09:31:17Z","publication_identifier":{"issn":["1461-1570"]},"author":[{"full_name":"Eick, B.","first_name":"B.","last_name":"Eick"},{"last_name":"Kirschmer","first_name":"Markus","full_name":"Kirschmer, Markus","id":"82258"},{"last_name":"Leedham-Green","first_name":"C.","full_name":"Leedham-Green, C."}],"title":"The constructive membership problem for discrete free subgroups of rank 2 of SL₂(R)","year":"2014","department":[{"_id":"102"}],"type":"journal_article","keyword":["Computational Theory and Mathematics","General Mathematics"],"date_created":"2023-03-07T08:30:15Z","extern":"1","abstract":[{"text":"We exhibit a practical algorithm for solving the constructive membership problem for discrete free subgroups of rank 2 in PSL₂(R) or SL₂(R). This algorithm, together with methods for checking whether a two-generator subgroup of PSL₂(R) or SL₂(R) is discrete and free, have been implemented in Magma for groups defined over real algebraic number fields.","lang":"eng"}],"publication":"LMS Journal of Computation and Mathematics","issue":"1","volume":17,"user_id":"93826","_id":"42794","publisher":"Wiley","page":"345-359","status":"public","citation":{"chicago":"Eick, B., Markus Kirschmer, and C. Leedham-Green. “The Constructive Membership Problem for Discrete Free Subgroups of Rank 2 of SL₂(R).” <i>LMS Journal of Computation and Mathematics</i> 17, no. 1 (2014): 345–59. <a href=\"https://doi.org/10.1112/s1461157014000047\">https://doi.org/10.1112/s1461157014000047</a>.","short":"B. Eick, M. Kirschmer, C. Leedham-Green, LMS Journal of Computation and Mathematics 17 (2014) 345–359.","apa":"Eick, B., Kirschmer, M., &#38; Leedham-Green, C. (2014). The constructive membership problem for discrete free subgroups of rank 2 of SL₂(R). <i>LMS Journal of Computation and Mathematics</i>, <i>17</i>(1), 345–359. <a href=\"https://doi.org/10.1112/s1461157014000047\">https://doi.org/10.1112/s1461157014000047</a>","ieee":"B. Eick, M. Kirschmer, and C. Leedham-Green, “The constructive membership problem for discrete free subgroups of rank 2 of SL₂(R),” <i>LMS Journal of Computation and Mathematics</i>, vol. 17, no. 1, pp. 345–359, 2014, doi: <a href=\"https://doi.org/10.1112/s1461157014000047\">10.1112/s1461157014000047</a>.","ama":"Eick B, Kirschmer M, Leedham-Green C. The constructive membership problem for discrete free subgroups of rank 2 of SL₂(R). <i>LMS Journal of Computation and Mathematics</i>. 2014;17(1):345-359. doi:<a href=\"https://doi.org/10.1112/s1461157014000047\">10.1112/s1461157014000047</a>","bibtex":"@article{Eick_Kirschmer_Leedham-Green_2014, title={The constructive membership problem for discrete free subgroups of rank 2 of SL₂(R)}, volume={17}, DOI={<a href=\"https://doi.org/10.1112/s1461157014000047\">10.1112/s1461157014000047</a>}, number={1}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Eick, B. and Kirschmer, Markus and Leedham-Green, C.}, year={2014}, pages={345–359} }","mla":"Eick, B., et al. “The Constructive Membership Problem for Discrete Free Subgroups of Rank 2 of SL₂(R).” <i>LMS Journal of Computation and Mathematics</i>, vol. 17, no. 1, Wiley, 2014, pp. 345–59, doi:<a href=\"https://doi.org/10.1112/s1461157014000047\">10.1112/s1461157014000047</a>."}},{"extern":"1","publication":"Journal of the London Mathematical Society","issue":"2","type":"journal_article","keyword":["General Mathematics"],"date_created":"2024-04-11T12:41:31Z","intvolume":"        88","date_updated":"2024-04-11T12:50:38Z","publication_status":"published","author":[{"id":"100450","full_name":"Gundlach, Fabian","first_name":"Fabian","last_name":"Gundlach"}],"publication_identifier":{"issn":["0024-6107"]},"title":"Integral Brauer-Manin obstructions for sums of two squares and a power","year":"2013","doi":"10.1112/jlms/jdt042","language":[{"iso":"eng"}],"citation":{"mla":"Gundlach, Fabian. “Integral Brauer-Manin Obstructions for Sums of Two Squares and a Power.” <i>Journal of the London Mathematical Society</i>, vol. 88, no. 2, Wiley, 2013, pp. 599–618, doi:<a href=\"https://doi.org/10.1112/jlms/jdt042\">10.1112/jlms/jdt042</a>.","bibtex":"@article{Gundlach_2013, title={Integral Brauer-Manin obstructions for sums of two squares and a power}, volume={88}, DOI={<a href=\"https://doi.org/10.1112/jlms/jdt042\">10.1112/jlms/jdt042</a>}, number={2}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Gundlach, Fabian}, year={2013}, pages={599–618} }","ama":"Gundlach F. Integral Brauer-Manin obstructions for sums of two squares and a power. <i>Journal of the London Mathematical Society</i>. 2013;88(2):599-618. doi:<a href=\"https://doi.org/10.1112/jlms/jdt042\">10.1112/jlms/jdt042</a>","ieee":"F. Gundlach, “Integral Brauer-Manin obstructions for sums of two squares and a power,” <i>Journal of the London Mathematical Society</i>, vol. 88, no. 2, pp. 599–618, 2013, doi: <a href=\"https://doi.org/10.1112/jlms/jdt042\">10.1112/jlms/jdt042</a>.","apa":"Gundlach, F. (2013). Integral Brauer-Manin obstructions for sums of two squares and a power. <i>Journal of the London Mathematical Society</i>, <i>88</i>(2), 599–618. <a href=\"https://doi.org/10.1112/jlms/jdt042\">https://doi.org/10.1112/jlms/jdt042</a>","short":"F. Gundlach, Journal of the London Mathematical Society 88 (2013) 599–618.","chicago":"Gundlach, Fabian. “Integral Brauer-Manin Obstructions for Sums of Two Squares and a Power.” <i>Journal of the London Mathematical Society</i> 88, no. 2 (2013): 599–618. <a href=\"https://doi.org/10.1112/jlms/jdt042\">https://doi.org/10.1112/jlms/jdt042</a>."},"status":"public","volume":88,"user_id":"100450","_id":"53419","publisher":"Wiley","page":"599-618"}]