[{"_id":"34916","department":[{"_id":"102"}],"user_id":"82258","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"publication":"Journal of Number Theory","type":"journal_article","abstract":[{"lang":"eng","text":"We describe the powers of irreducible polynomials occurring as characteristic polynomials of automorphisms of even unimodular lattices over number fields. This generalizes results of Gross & McMullen and Bayer-Fluckiger & Taelman."}],"status":"public","publisher":"Elsevier BV","date_updated":"2023-12-06T10:07:17Z","volume":197,"date_created":"2022-12-23T11:04:34Z","author":[{"full_name":"Kirschmer, Markus","id":"82258","last_name":"Kirschmer","first_name":"Markus"}],"title":"Automorphisms of even unimodular lattices over number fields","doi":"10.1016/j.jnt.2018.08.004","publication_identifier":{"issn":["0022-314X"]},"publication_status":"published","year":"2019","intvolume":"       197","page":"121-134","citation":{"bibtex":"@article{Kirschmer_2019, title={Automorphisms of even unimodular lattices over number fields}, volume={197}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">10.1016/j.jnt.2018.08.004</a>}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer, Markus}, year={2019}, pages={121–134} }","mla":"Kirschmer, Markus. “Automorphisms of Even Unimodular Lattices over Number Fields.” <i>Journal of Number Theory</i>, vol. 197, Elsevier BV, 2019, pp. 121–34, doi:<a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">10.1016/j.jnt.2018.08.004</a>.","short":"M. Kirschmer, Journal of Number Theory 197 (2019) 121–134.","apa":"Kirschmer, M. (2019). Automorphisms of even unimodular lattices over number fields. <i>Journal of Number Theory</i>, <i>197</i>, 121–134. <a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">https://doi.org/10.1016/j.jnt.2018.08.004</a>","ieee":"M. Kirschmer, “Automorphisms of even unimodular lattices over number fields,” <i>Journal of Number Theory</i>, vol. 197, pp. 121–134, 2019, doi: <a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">10.1016/j.jnt.2018.08.004</a>.","chicago":"Kirschmer, Markus. “Automorphisms of Even Unimodular Lattices over Number Fields.” <i>Journal of Number Theory</i> 197 (2019): 121–34. <a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">https://doi.org/10.1016/j.jnt.2018.08.004</a>.","ama":"Kirschmer M. Automorphisms of even unimodular lattices over number fields. <i>Journal of Number Theory</i>. 2019;197:121-134. doi:<a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">10.1016/j.jnt.2018.08.004</a>"}},{"department":[{"_id":"102"}],"user_id":"106108","_id":"55284","extern":"1","language":[{"iso":"eng"}],"publication":"Mathematika","type":"journal_article","status":"public","volume":64,"date_created":"2024-07-16T11:09:02Z","author":[{"first_name":"Ch.","last_name":"Elsholtz","full_name":"Elsholtz, Ch."},{"first_name":"Marc","orcid":"0000-0001-9650-2459","last_name":"Technau","id":"106108","full_name":"Technau, Marc"},{"full_name":"Technau, N.","last_name":"Technau","first_name":"N."}],"date_updated":"2024-07-24T07:25:42Z","doi":"10.1112/S0025579319000214","title":"The maximal order of iterated multiplicative functions","issue":"4","page":"990–1009","intvolume":"        64","citation":{"short":"Ch. Elsholtz, M. Technau, N. Technau, Mathematika 64 (2019) 990–1009.","mla":"Elsholtz, Ch., et al. “The Maximal Order of Iterated Multiplicative Functions.” <i>Mathematika</i>, vol. 64, no. 4, 2019, pp. 990–1009, doi:<a href=\"https://doi.org/10.1112/S0025579319000214\">10.1112/S0025579319000214</a>.","bibtex":"@article{Elsholtz_Technau_Technau_2019, title={The maximal order of iterated multiplicative functions}, volume={64}, DOI={<a href=\"https://doi.org/10.1112/S0025579319000214\">10.1112/S0025579319000214</a>}, number={4}, journal={Mathematika}, author={Elsholtz, Ch. and Technau, Marc and Technau, N.}, year={2019}, pages={990–1009} }","apa":"Elsholtz, Ch., Technau, M., &#38; Technau, N. (2019). The maximal order of iterated multiplicative functions. <i>Mathematika</i>, <i>64</i>(4), 990–1009. <a href=\"https://doi.org/10.1112/S0025579319000214\">https://doi.org/10.1112/S0025579319000214</a>","ama":"Elsholtz Ch, Technau M, Technau N. The maximal order of iterated multiplicative functions. <i>Mathematika</i>. 2019;64(4):990–1009. doi:<a href=\"https://doi.org/10.1112/S0025579319000214\">10.1112/S0025579319000214</a>","ieee":"Ch. Elsholtz, M. Technau, and N. Technau, “The maximal order of iterated multiplicative functions,” <i>Mathematika</i>, vol. 64, no. 4, pp. 990–1009, 2019, doi: <a href=\"https://doi.org/10.1112/S0025579319000214\">10.1112/S0025579319000214</a>.","chicago":"Elsholtz, Ch., Marc Technau, and N. Technau. “The Maximal Order of Iterated Multiplicative Functions.” <i>Mathematika</i> 64, no. 4 (2019): 990–1009. <a href=\"https://doi.org/10.1112/S0025579319000214\">https://doi.org/10.1112/S0025579319000214</a>."},"year":"2019"},{"status":"public","publication":"Notes Number Theory Discrete Math.","type":"journal_article","extern":"1","language":[{"iso":"eng"}],"_id":"55285","department":[{"_id":"102"}],"user_id":"106108","year":"2019","intvolume":"        25","page":"127–135","citation":{"mla":"Technau, Marc. “Generalised Beatty Sets.” <i>Notes Number Theory Discrete Math.</i>, vol. 25, no. 2, 2019, pp. 127–135, doi:<a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">10.7546/nntdm.2019.25.2.127-135</a>.","short":"M. Technau, Notes Number Theory Discrete Math. 25 (2019) 127–135.","bibtex":"@article{Technau_2019, title={Generalised Beatty sets}, volume={25}, DOI={<a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">10.7546/nntdm.2019.25.2.127-135</a>}, number={2}, journal={Notes Number Theory Discrete Math.}, author={Technau, Marc}, year={2019}, pages={127–135} }","apa":"Technau, M. (2019). Generalised Beatty sets. <i>Notes Number Theory Discrete Math.</i>, <i>25</i>(2), 127–135. <a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">https://doi.org/10.7546/nntdm.2019.25.2.127-135</a>","ama":"Technau M. Generalised Beatty sets. <i>Notes Number Theory Discrete Math</i>. 2019;25(2):127–135. doi:<a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">10.7546/nntdm.2019.25.2.127-135</a>","chicago":"Technau, Marc. “Generalised Beatty Sets.” <i>Notes Number Theory Discrete Math.</i> 25, no. 2 (2019): 127–135. <a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">https://doi.org/10.7546/nntdm.2019.25.2.127-135</a>.","ieee":"M. Technau, “Generalised Beatty sets,” <i>Notes Number Theory Discrete Math.</i>, vol. 25, no. 2, pp. 127–135, 2019, doi: <a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">10.7546/nntdm.2019.25.2.127-135</a>."},"issue":"2","title":"Generalised Beatty sets","doi":"10.7546/nntdm.2019.25.2.127-135","date_updated":"2024-07-24T07:25:59Z","volume":25,"author":[{"first_name":"Marc","id":"106108","full_name":"Technau, Marc","orcid":"0000-0001-9650-2459","last_name":"Technau"}],"date_created":"2024-07-16T11:09:02Z"},{"year":"2019","issue":"4","title":"Determinant groups of Hermitian lattices over local fields","publisher":"Springer Science and Business Media LLC","date_created":"2022-12-23T11:03:41Z","abstract":[{"text":"We describe the determinants of the automorphism groups of Hermitian lattices over local fields. Using a result of G. Shimura, this yields an explicit method to compute the special genera in a given genus of Hermitian lattices over a number field.","lang":"eng"}],"publication":"Archiv der Mathematik","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"citation":{"chicago":"Kirschmer, Markus. “Determinant Groups of Hermitian Lattices over Local Fields.” <i>Archiv Der Mathematik</i> 113, no. 4 (2019): 337–47. <a href=\"https://doi.org/10.1007/s00013-019-01348-z\">https://doi.org/10.1007/s00013-019-01348-z</a>.","ieee":"M. Kirschmer, “Determinant groups of Hermitian lattices over local fields,” <i>Archiv der Mathematik</i>, vol. 113, no. 4, pp. 337–347, 2019, doi: <a href=\"https://doi.org/10.1007/s00013-019-01348-z\">10.1007/s00013-019-01348-z</a>.","ama":"Kirschmer M. Determinant groups of Hermitian lattices over local fields. <i>Archiv der Mathematik</i>. 2019;113(4):337-347. doi:<a href=\"https://doi.org/10.1007/s00013-019-01348-z\">10.1007/s00013-019-01348-z</a>","bibtex":"@article{Kirschmer_2019, title={Determinant groups of Hermitian lattices over local fields}, volume={113}, DOI={<a href=\"https://doi.org/10.1007/s00013-019-01348-z\">10.1007/s00013-019-01348-z</a>}, number={4}, journal={Archiv der Mathematik}, publisher={Springer Science and Business Media LLC}, author={Kirschmer, Markus}, year={2019}, pages={337–347} }","mla":"Kirschmer, Markus. “Determinant Groups of Hermitian Lattices over Local Fields.” <i>Archiv Der Mathematik</i>, vol. 113, no. 4, Springer Science and Business Media LLC, 2019, pp. 337–47, doi:<a href=\"https://doi.org/10.1007/s00013-019-01348-z\">10.1007/s00013-019-01348-z</a>.","short":"M. Kirschmer, Archiv Der Mathematik 113 (2019) 337–347.","apa":"Kirschmer, M. (2019). Determinant groups of Hermitian lattices over local fields. <i>Archiv Der Mathematik</i>, <i>113</i>(4), 337–347. <a href=\"https://doi.org/10.1007/s00013-019-01348-z\">https://doi.org/10.1007/s00013-019-01348-z</a>"},"intvolume":"       113","page":"337-347","publication_status":"published","publication_identifier":{"issn":["0003-889X","1420-8938"]},"doi":"10.1007/s00013-019-01348-z","date_updated":"2023-04-04T09:05:04Z","author":[{"id":"82258","full_name":"Kirschmer, Markus","last_name":"Kirschmer","first_name":"Markus"}],"volume":113,"status":"public","type":"journal_article","_id":"34915","user_id":"93826","department":[{"_id":"102"}]},{"supervisor":[{"full_name":"Steuding, Jörn","last_name":"Steuding","first_name":"Jörn"}],"author":[{"id":"106108","full_name":"Technau, Marc","orcid":"0000-0001-9650-2459","last_name":"Technau","first_name":"Marc"}],"date_created":"2024-07-16T11:09:19Z","date_updated":"2024-07-24T07:24:57Z","publisher":"University of Würzburg","doi":"10.25972/WUP-978-3-95826-089-4","title":"On Beatty sets and some generalisations thereof","citation":{"ieee":"M. Technau, <i>On Beatty sets and some generalisations thereof</i>. Würzburg: University of Würzburg, 2018.","chicago":"Technau, Marc. <i>On Beatty Sets and Some Generalisations Thereof</i>. Würzburg: University of Würzburg, 2018. <a href=\"https://doi.org/10.25972/WUP-978-3-95826-089-4\">https://doi.org/10.25972/WUP-978-3-95826-089-4</a>.","ama":"Technau M. <i>On Beatty Sets and Some Generalisations Thereof</i>. University of Würzburg; 2018. doi:<a href=\"https://doi.org/10.25972/WUP-978-3-95826-089-4\">10.25972/WUP-978-3-95826-089-4</a>","bibtex":"@book{Technau_2018, place={Würzburg}, title={On Beatty sets and some generalisations thereof}, DOI={<a href=\"https://doi.org/10.25972/WUP-978-3-95826-089-4\">10.25972/WUP-978-3-95826-089-4</a>}, publisher={University of Würzburg}, author={Technau, Marc}, year={2018} }","mla":"Technau, Marc. <i>On Beatty Sets and Some Generalisations Thereof</i>. University of Würzburg, 2018, doi:<a href=\"https://doi.org/10.25972/WUP-978-3-95826-089-4\">10.25972/WUP-978-3-95826-089-4</a>.","short":"M. Technau, On Beatty Sets and Some Generalisations Thereof, University of Würzburg, Würzburg, 2018.","apa":"Technau, M. (2018). <i>On Beatty sets and some generalisations thereof</i>. University of Würzburg. <a href=\"https://doi.org/10.25972/WUP-978-3-95826-089-4\">https://doi.org/10.25972/WUP-978-3-95826-089-4</a>"},"place":"Würzburg","year":"2018","user_id":"106108","department":[{"_id":"102"}],"_id":"55291","extern":"1","language":[{"iso":"eng"}],"type":"dissertation","status":"public"},{"year":"2018","title":"Computing subfields of number fields and applications to Galois group computations","date_created":"2022-12-22T10:52:18Z","publisher":"Elsevier BV","abstract":[{"text":"A polynomial time algorithm to find generators of the lattice of all subfields of a given number field was given in van Hoeij et al. (2013).\r\n\r\nThis article reports on a massive speedup of this algorithm. This is primary achieved by our new concept of Galois-generating subfields. In general this is a very small set of subfields that determine all other subfields in a group-theoretic way. We compute them by targeted calls to the method from van Hoeij et al. (2013). For an early termination of these calls, we give a list of criteria that imply that further calls will not result in additional subfields.\r\n\r\nFinally, we explain how we use subfields to get a good starting group for the computation of Galois groups.","lang":"eng"}],"publication":"Journal of Symbolic Computation","language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"],"external_id":{"arxiv":["1610.06837 "]},"intvolume":"        93","page":"1-20","citation":{"ieee":"A.-S. Elsenhans and J. Klüners, “Computing subfields of number fields and applications to Galois group computations,” <i>Journal of Symbolic Computation</i>, vol. 93, pp. 1–20, 2018, doi: <a href=\"https://doi.org/10.1016/j.jsc.2018.04.013\">10.1016/j.jsc.2018.04.013</a>.","chicago":"Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Subfields of Number Fields and Applications to Galois Group Computations.” <i>Journal of Symbolic Computation</i> 93 (2018): 1–20. <a href=\"https://doi.org/10.1016/j.jsc.2018.04.013\">https://doi.org/10.1016/j.jsc.2018.04.013</a>.","ama":"Elsenhans A-S, Klüners J. Computing subfields of number fields and applications to Galois group computations. <i>Journal of Symbolic Computation</i>. 2018;93:1-20. doi:<a href=\"https://doi.org/10.1016/j.jsc.2018.04.013\">10.1016/j.jsc.2018.04.013</a>","bibtex":"@article{Elsenhans_Klüners_2018, title={Computing subfields of number fields and applications to Galois group computations}, volume={93}, DOI={<a href=\"https://doi.org/10.1016/j.jsc.2018.04.013\">10.1016/j.jsc.2018.04.013</a>}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Elsenhans, Andreas-Stephan and Klüners, Jürgen}, year={2018}, pages={1–20} }","short":"A.-S. Elsenhans, J. Klüners, Journal of Symbolic Computation 93 (2018) 1–20.","mla":"Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Subfields of Number Fields and Applications to Galois Group Computations.” <i>Journal of Symbolic Computation</i>, vol. 93, Elsevier BV, 2018, pp. 1–20, doi:<a href=\"https://doi.org/10.1016/j.jsc.2018.04.013\">10.1016/j.jsc.2018.04.013</a>.","apa":"Elsenhans, A.-S., &#38; Klüners, J. (2018). Computing subfields of number fields and applications to Galois group computations. <i>Journal of Symbolic Computation</i>, <i>93</i>, 1–20. <a href=\"https://doi.org/10.1016/j.jsc.2018.04.013\">https://doi.org/10.1016/j.jsc.2018.04.013</a>"},"publication_identifier":{"issn":["0747-7171"]},"publication_status":"published","doi":"10.1016/j.jsc.2018.04.013","volume":93,"author":[{"first_name":"Andreas-Stephan","last_name":"Elsenhans","full_name":"Elsenhans, Andreas-Stephan"},{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"}],"date_updated":"2023-03-06T09:05:51Z","status":"public","type":"journal_article","department":[{"_id":"102"}],"user_id":"93826","_id":"34843"},{"status":"public","abstract":[{"text":"We classify all one-class genera of admissible lattice chains of length at least 2 in hermitian spaces over number fields. If L is a lattice in the chain and p the prime ideal dividing the index of the lattices in the chain, then the {p}-arithmetic group Aut(L{p}) acts chamber transitively on the corresponding Bruhat-Tits building. So our classification provides a step forward to a complete classification of these chamber transitive groups which has been announced 1987 (without a detailed proof) by Kantor, Liebler and Tits. In fact we find all their groups over number fields and one additional building with a discrete chamber transitive group.","lang":"eng"}],"publication":"Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory","type":"book_chapter","language":[{"iso":"eng"}],"extern":"1","department":[{"_id":"102"}],"user_id":"93826","_id":"42788","citation":{"ama":"Kirschmer M, Nebe G. One Class Genera of Lattice Chains Over Number Fields. In: <i>Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory</i>. Springer International Publishing; 2018. doi:<a href=\"https://doi.org/10.1007/978-3-319-70566-8_22\">10.1007/978-3-319-70566-8_22</a>","chicago":"Kirschmer, Markus, and Gabriele Nebe. “One Class Genera of Lattice Chains Over Number Fields.” In <i>Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory</i>. Cham: Springer International Publishing, 2018. <a href=\"https://doi.org/10.1007/978-3-319-70566-8_22\">https://doi.org/10.1007/978-3-319-70566-8_22</a>.","ieee":"M. Kirschmer and G. Nebe, “One Class Genera of Lattice Chains Over Number Fields,” in <i>Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory</i>, Cham: Springer International Publishing, 2018.","mla":"Kirschmer, Markus, and Gabriele Nebe. “One Class Genera of Lattice Chains Over Number Fields.” <i>Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory</i>, Springer International Publishing, 2018, doi:<a href=\"https://doi.org/10.1007/978-3-319-70566-8_22\">10.1007/978-3-319-70566-8_22</a>.","bibtex":"@inbook{Kirschmer_Nebe_2018, place={Cham}, title={One Class Genera of Lattice Chains Over Number Fields}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-70566-8_22\">10.1007/978-3-319-70566-8_22</a>}, booktitle={Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory}, publisher={Springer International Publishing}, author={Kirschmer, Markus and Nebe, Gabriele}, year={2018} }","short":"M. Kirschmer, G. Nebe, in: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, Springer International Publishing, Cham, 2018.","apa":"Kirschmer, M., &#38; Nebe, G. (2018). One Class Genera of Lattice Chains Over Number Fields. In <i>Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory</i>. Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-319-70566-8_22\">https://doi.org/10.1007/978-3-319-70566-8_22</a>"},"place":"Cham","year":"2018","publication_identifier":{"isbn":["9783319705651","9783319705668"]},"publication_status":"published","doi":"10.1007/978-3-319-70566-8_22","title":"One Class Genera of Lattice Chains Over Number Fields","author":[{"full_name":"Kirschmer, Markus","id":"82258","last_name":"Kirschmer","first_name":"Markus"},{"last_name":"Nebe","full_name":"Nebe, Gabriele","first_name":"Gabriele"}],"date_created":"2023-03-07T08:23:48Z","publisher":"Springer International Publishing","date_updated":"2023-04-04T09:08:19Z"},{"status":"public","abstract":[{"text":"We show that exceptional algebraic groups over number fields do not admit one-class genera of parahoric groups, except in the case G₂ . For the group G₂, we enumerate all such one-class genera for the usual seven-dimensional representation.","lang":"eng"}],"type":"journal_article","publication":"Journal de Théorie des Nombres de Bordeaux","extern":"1","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"user_id":"93826","department":[{"_id":"102"}],"_id":"42790","citation":{"ieee":"M. Kirschmer, “One-class genera of exceptional groups over number fields,” <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 30, no. 3, pp. 847–857, 2018, doi: <a href=\"https://doi.org/10.5802/jtnb.1052\">10.5802/jtnb.1052</a>.","chicago":"Kirschmer, Markus. “One-Class Genera of Exceptional Groups over Number Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i> 30, no. 3 (2018): 847–57. <a href=\"https://doi.org/10.5802/jtnb.1052\">https://doi.org/10.5802/jtnb.1052</a>.","ama":"Kirschmer M. One-class genera of exceptional groups over number fields. <i>Journal de Théorie des Nombres de Bordeaux</i>. 2018;30(3):847-857. doi:<a href=\"https://doi.org/10.5802/jtnb.1052\">10.5802/jtnb.1052</a>","apa":"Kirschmer, M. (2018). One-class genera of exceptional groups over number fields. <i>Journal de Théorie Des Nombres de Bordeaux</i>, <i>30</i>(3), 847–857. <a href=\"https://doi.org/10.5802/jtnb.1052\">https://doi.org/10.5802/jtnb.1052</a>","short":"M. Kirschmer, Journal de Théorie Des Nombres de Bordeaux 30 (2018) 847–857.","bibtex":"@article{Kirschmer_2018, title={One-class genera of exceptional groups over number fields}, volume={30}, DOI={<a href=\"https://doi.org/10.5802/jtnb.1052\">10.5802/jtnb.1052</a>}, number={3}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule MathDoc/CEDRAM}, author={Kirschmer, Markus}, year={2018}, pages={847–857} }","mla":"Kirschmer, Markus. “One-Class Genera of Exceptional Groups over Number Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i>, vol. 30, no. 3, Cellule MathDoc/CEDRAM, 2018, pp. 847–57, doi:<a href=\"https://doi.org/10.5802/jtnb.1052\">10.5802/jtnb.1052</a>."},"intvolume":"        30","page":"847-857","year":"2018","issue":"3","publication_status":"published","publication_identifier":{"issn":["1246-7405","2118-8572"]},"doi":"10.5802/jtnb.1052","title":"One-class genera of exceptional groups over number fields","author":[{"first_name":"Markus","last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus"}],"date_created":"2023-03-07T08:27:36Z","volume":30,"date_updated":"2023-04-04T09:07:32Z","publisher":"Cellule MathDoc/CEDRAM"},{"user_id":"106108","department":[{"_id":"102"}],"_id":"55293","language":[{"iso":"eng"}],"extern":"1","type":"report","status":"public","author":[{"full_name":"Barth, D.","last_name":"Barth","first_name":"D."},{"first_name":"M.","last_name":"Beck","full_name":"Beck, M."},{"first_name":"T.","last_name":"Dose","full_name":"Dose, T."},{"first_name":"Ch.","last_name":"Glaßer","full_name":"Glaßer, Ch."},{"last_name":"Michler","full_name":"Michler, L.","first_name":"L."},{"id":"106108","full_name":"Technau, Marc","orcid":"0000-0001-9650-2459","last_name":"Technau","first_name":"Marc"}],"date_created":"2024-07-16T11:09:20Z","date_updated":"2024-07-24T07:24:26Z","title":"Emptiness problems for integer circuits","citation":{"apa":"Barth, D., Beck, M., Dose, T., Glaßer, Ch., Michler, L., &#38; Technau, M. (2017). <i>Emptiness problems for integer circuits</i>.","mla":"Barth, D., et al. <i>Emptiness Problems for Integer Circuits</i>. 2017.","bibtex":"@book{Barth_Beck_Dose_Glaßer_Michler_Technau_2017, place={https://eccc.weizmann.ac.il/report/2017/012}, title={Emptiness problems for integer circuits}, author={Barth, D. and Beck, M. and Dose, T. and Glaßer, Ch. and Michler, L. and Technau, Marc}, year={2017} }","short":"D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, M. Technau, Emptiness Problems for Integer Circuits, https://eccc.weizmann.ac.il/report/2017/012, 2017.","ieee":"D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, and M. Technau, <i>Emptiness problems for integer circuits</i>. https://eccc.weizmann.ac.il/report/2017/012, 2017.","chicago":"Barth, D., M. Beck, T. Dose, Ch. Glaßer, L. Michler, and Marc Technau. <i>Emptiness Problems for Integer Circuits</i>. https://eccc.weizmann.ac.il/report/2017/012, 2017.","ama":"Barth D, Beck M, Dose T, Glaßer Ch, Michler L, Technau M. <i>Emptiness Problems for Integer Circuits</i>.; 2017."},"place":"https://eccc.weizmann.ac.il/report/2017/012","year":"2017"},{"editor":[{"first_name":"Kim G.","full_name":"Larsen, Kim G.","last_name":"Larsen"},{"first_name":"Hans L.","full_name":"Bodlaender, Hans L.","last_name":"Bodlaender"},{"last_name":"Raskin","full_name":"Raskin, Jean-Francois","first_name":"Jean-Francois"}],"status":"public","publication":"42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)","type":"conference","extern":"1","language":[{"iso":"eng"}],"_id":"55292","department":[{"_id":"102"}],"series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","user_id":"106108","year":"2017","intvolume":"        83","page":"33:1–33:14","citation":{"short":"D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, M. Technau, in: K.G. Larsen, H.L. Bodlaender, J.-F. Raskin (Eds.), 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017), Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 2017, p. 33:1–33:14.","bibtex":"@inproceedings{Barth_Beck_Dose_Glaßer_Michler_Technau_2017, series={Leibniz International Proceedings in Informatics (LIPIcs)}, title={Emptiness problems for integer circuits}, volume={83}, DOI={<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.33\">10.4230/LIPIcs.MFCS.2017.33</a>}, booktitle={42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)}, publisher={Schloss Dagstuhl–Leibniz-Zentrum für Informatik}, author={Barth, D. and Beck, M. and Dose, T. and Glaßer, Ch. and Michler, L. and Technau, Marc}, editor={Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois}, year={2017}, pages={33:1–33:14}, collection={Leibniz International Proceedings in Informatics (LIPIcs)} }","mla":"Barth, D., et al. “Emptiness Problems for Integer Circuits.” <i>42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)</i>, edited by Kim G. Larsen et al., vol. 83, Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 2017, p. 33:1–33:14, doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.33\">10.4230/LIPIcs.MFCS.2017.33</a>.","apa":"Barth, D., Beck, M., Dose, T., Glaßer, Ch., Michler, L., &#38; Technau, M. (2017). Emptiness problems for integer circuits. In K. G. Larsen, H. L. Bodlaender, &#38; J.-F. Raskin (Eds.), <i>42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)</i> (Vol. 83, p. 33:1–33:14). Schloss Dagstuhl–Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.33\">https://doi.org/10.4230/LIPIcs.MFCS.2017.33</a>","chicago":"Barth, D., M. Beck, T. Dose, Ch. Glaßer, L. Michler, and Marc Technau. “Emptiness Problems for Integer Circuits.” In <i>42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)</i>, edited by Kim G. Larsen, Hans L. Bodlaender, and Jean-Francois Raskin, 83:33:1–33:14. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 2017. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.33\">https://doi.org/10.4230/LIPIcs.MFCS.2017.33</a>.","ieee":"D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, and M. Technau, “Emptiness problems for integer circuits,” in <i>42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)</i>, 2017, vol. 83, p. 33:1–33:14, doi: <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.33\">10.4230/LIPIcs.MFCS.2017.33</a>.","ama":"Barth D, Beck M, Dose T, Glaßer Ch, Michler L, Technau M. Emptiness problems for integer circuits. In: Larsen KG, Bodlaender HL, Raskin J-F, eds. <i>42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)</i>. Vol 83. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl–Leibniz-Zentrum für Informatik; 2017:33:1–33:14. doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.33\">10.4230/LIPIcs.MFCS.2017.33</a>"},"title":"Emptiness problems for integer circuits","doi":"10.4230/LIPIcs.MFCS.2017.33","publisher":"Schloss Dagstuhl–Leibniz-Zentrum für Informatik","date_updated":"2024-07-24T07:25:35Z","volume":83,"date_created":"2024-07-16T11:09:20Z","author":[{"first_name":"D.","full_name":"Barth, D.","last_name":"Barth"},{"first_name":"M.","full_name":"Beck, M.","last_name":"Beck"},{"first_name":"T.","last_name":"Dose","full_name":"Dose, T."},{"full_name":"Glaßer, Ch.","last_name":"Glaßer","first_name":"Ch."},{"full_name":"Michler, L.","last_name":"Michler","first_name":"L."},{"full_name":"Technau, Marc","id":"106108","last_name":"Technau","orcid":"0000-0001-9650-2459","first_name":"Marc"}]},{"language":[{"iso":"eng"}],"department":[{"_id":"102"}],"user_id":"106108","_id":"55275","status":"public","publication":"Comput. Methods Funct. Theory","type":"journal_article","doi":"10.1007/s40315-016-0179-6","title":"A Loewner equation for infinitely many slits","volume":17,"date_created":"2024-07-16T11:08:06Z","author":[{"first_name":"Marc","id":"106108","full_name":"Technau, Marc","orcid":"0000-0001-9650-2459","last_name":"Technau"},{"full_name":"Technau, N.","last_name":"Technau","first_name":"N."}],"date_updated":"2024-07-24T07:24:37Z","intvolume":"        17","page":"255–272","citation":{"short":"M. Technau, N. Technau, Comput. Methods Funct. Theory 17 (2017) 255–272.","mla":"Technau, Marc, and N. Technau. “A Loewner Equation for Infinitely Many Slits.” <i>Comput. Methods Funct. Theory</i>, vol. 17, no. 2, 2017, pp. 255–272, doi:<a href=\"https://doi.org/10.1007/s40315-016-0179-6\">10.1007/s40315-016-0179-6</a>.","bibtex":"@article{Technau_Technau_2017, title={A Loewner equation for infinitely many slits}, volume={17}, DOI={<a href=\"https://doi.org/10.1007/s40315-016-0179-6\">10.1007/s40315-016-0179-6</a>}, number={2}, journal={Comput. Methods Funct. Theory}, author={Technau, Marc and Technau, N.}, year={2017}, pages={255–272} }","apa":"Technau, M., &#38; Technau, N. (2017). A Loewner equation for infinitely many slits. <i>Comput. Methods Funct. Theory</i>, <i>17</i>(2), 255–272. <a href=\"https://doi.org/10.1007/s40315-016-0179-6\">https://doi.org/10.1007/s40315-016-0179-6</a>","ama":"Technau M, Technau N. A Loewner equation for infinitely many slits. <i>Comput Methods Funct Theory</i>. 2017;17(2):255–272. doi:<a href=\"https://doi.org/10.1007/s40315-016-0179-6\">10.1007/s40315-016-0179-6</a>","ieee":"M. Technau and N. Technau, “A Loewner equation for infinitely many slits,” <i>Comput. Methods Funct. Theory</i>, vol. 17, no. 2, pp. 255–272, 2017, doi: <a href=\"https://doi.org/10.1007/s40315-016-0179-6\">10.1007/s40315-016-0179-6</a>.","chicago":"Technau, Marc, and N. Technau. “A Loewner Equation for Infinitely Many Slits.” <i>Comput. Methods Funct. Theory</i> 17, no. 2 (2017): 255–272. <a href=\"https://doi.org/10.1007/s40315-016-0179-6\">https://doi.org/10.1007/s40315-016-0179-6</a>."},"year":"2017","issue":"2"},{"type":"journal_article","status":"public","_id":"42791","user_id":"93826","department":[{"_id":"102"}],"extern":"1","publication_status":"published","publication_identifier":{"issn":["0021-8693"]},"citation":{"ieee":"M. Kirschmer and M. G. Rüther, “The constructive membership problem for discrete two-generator subgroups of SL(2,R),” <i>Journal of Algebra</i>, vol. 480, pp. 519–548, 2017, doi: <a href=\"https://doi.org/10.1016/j.jalgebra.2017.02.029\">10.1016/j.jalgebra.2017.02.029</a>.","chicago":"Kirschmer, Markus, and Marion G. Rüther. “The Constructive Membership Problem for Discrete Two-Generator Subgroups of SL(2,R).” <i>Journal of Algebra</i> 480 (2017): 519–48. <a href=\"https://doi.org/10.1016/j.jalgebra.2017.02.029\">https://doi.org/10.1016/j.jalgebra.2017.02.029</a>.","ama":"Kirschmer M, Rüther MG. The constructive membership problem for discrete two-generator subgroups of SL(2,R). <i>Journal of Algebra</i>. 2017;480:519-548. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2017.02.029\">10.1016/j.jalgebra.2017.02.029</a>","apa":"Kirschmer, M., &#38; Rüther, M. G. (2017). The constructive membership problem for discrete two-generator subgroups of SL(2,R). <i>Journal of Algebra</i>, <i>480</i>, 519–548. <a href=\"https://doi.org/10.1016/j.jalgebra.2017.02.029\">https://doi.org/10.1016/j.jalgebra.2017.02.029</a>","mla":"Kirschmer, Markus, and Marion G. Rüther. “The Constructive Membership Problem for Discrete Two-Generator Subgroups of SL(2,R).” <i>Journal of Algebra</i>, vol. 480, Elsevier BV, 2017, pp. 519–48, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2017.02.029\">10.1016/j.jalgebra.2017.02.029</a>.","bibtex":"@article{Kirschmer_Rüther_2017, title={The constructive membership problem for discrete two-generator subgroups of SL(2,R)}, volume={480}, DOI={<a href=\"https://doi.org/10.1016/j.jalgebra.2017.02.029\">10.1016/j.jalgebra.2017.02.029</a>}, journal={Journal of Algebra}, publisher={Elsevier BV}, author={Kirschmer, Markus and Rüther, Marion G.}, year={2017}, pages={519–548} }","short":"M. Kirschmer, M.G. Rüther, Journal of Algebra 480 (2017) 519–548."},"intvolume":"       480","page":"519-548","date_updated":"2023-04-04T09:10:14Z","author":[{"last_name":"Kirschmer","full_name":"Kirschmer, Markus","id":"82258","first_name":"Markus"},{"first_name":"Marion G.","last_name":"Rüther","full_name":"Rüther, Marion G."}],"volume":480,"doi":"10.1016/j.jalgebra.2017.02.029","publication":"Journal of Algebra","abstract":[{"text":"We describe a practical algorithm to solve the constructive membership problem for discrete two-generator subgroups of SL₂(R) or PSL₂(R). This algorithm has been implemented in Magma for groups defined over real algebraic number fields.","lang":"eng"}],"keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"year":"2017","publisher":"Elsevier BV","date_created":"2023-03-07T08:28:11Z","title":"The constructive membership problem for discrete two-generator subgroups of SL(2,R)"},{"status":"public","type":"journal_article","publication":"J. Number Theory","extern":"1","language":[{"iso":"eng"}],"user_id":"106108","department":[{"_id":"102"}],"_id":"55281","citation":{"bibtex":"@article{Steuding_Technau_2016, title={The least prime number in a Beatty sequence}, volume={169}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2016.05.022\">10.1016/j.jnt.2016.05.022</a>}, journal={J. Number Theory}, author={Steuding, J. and Technau, Marc}, year={2016}, pages={144–159} }","mla":"Steuding, J., and Marc Technau. “The Least Prime Number in a Beatty Sequence.” <i>J. Number Theory</i>, vol. 169, 2016, pp. 144–159, doi:<a href=\"https://doi.org/10.1016/j.jnt.2016.05.022\">10.1016/j.jnt.2016.05.022</a>.","short":"J. Steuding, M. Technau, J. Number Theory 169 (2016) 144–159.","apa":"Steuding, J., &#38; Technau, M. (2016). The least prime number in a Beatty sequence. <i>J. Number Theory</i>, <i>169</i>, 144–159. <a href=\"https://doi.org/10.1016/j.jnt.2016.05.022\">https://doi.org/10.1016/j.jnt.2016.05.022</a>","ieee":"J. Steuding and M. Technau, “The least prime number in a Beatty sequence,” <i>J. Number Theory</i>, vol. 169, pp. 144–159, 2016, doi: <a href=\"https://doi.org/10.1016/j.jnt.2016.05.022\">10.1016/j.jnt.2016.05.022</a>.","chicago":"Steuding, J., and Marc Technau. “The Least Prime Number in a Beatty Sequence.” <i>J. Number Theory</i> 169 (2016): 144–159. <a href=\"https://doi.org/10.1016/j.jnt.2016.05.022\">https://doi.org/10.1016/j.jnt.2016.05.022</a>.","ama":"Steuding J, Technau M. The least prime number in a Beatty sequence. <i>J Number Theory</i>. 2016;169:144–159. doi:<a href=\"https://doi.org/10.1016/j.jnt.2016.05.022\">10.1016/j.jnt.2016.05.022</a>"},"page":"144–159","intvolume":"       169","year":"2016","doi":"10.1016/j.jnt.2016.05.022","title":"The least prime number in a Beatty sequence","date_created":"2024-07-16T11:09:01Z","author":[{"last_name":"Steuding","full_name":"Steuding, J.","first_name":"J."},{"first_name":"Marc","full_name":"Technau, Marc","id":"106108","last_name":"Technau","orcid":"0000-0001-9650-2459"}],"volume":169,"date_updated":"2024-07-24T07:26:27Z"},{"publisher":"Elsevier BV","date_created":"2022-12-22T10:52:47Z","title":"Are number fields determined by Artin L-functions?","year":"2016","external_id":{"arxiv":["1509.06883 "]},"keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"publication":"Journal of Number Theory","abstract":[{"lang":"eng","text":"Let k be a number field, K/k a finite Galois extension with Galois group G, χ a faithful character of G. We prove that the Artin L-function L(s,χ,K/k) determines the Galois closure of K over $\\ℚ$. In the special case $k=\\ℚ$ it also determines the character χ. "}],"date_updated":"2023-03-06T10:44:22Z","author":[{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"},{"last_name":"Nicolae","full_name":"Nicolae, Florin","first_name":"Florin"}],"volume":167,"doi":"10.1016/j.jnt.2016.03.023","publication_status":"published","publication_identifier":{"issn":["0022-314X"]},"citation":{"ama":"Klüners J, Nicolae F. Are number fields determined by Artin L-functions? <i>Journal of Number Theory</i>. 2016;167:161-168. doi:<a href=\"https://doi.org/10.1016/j.jnt.2016.03.023\">10.1016/j.jnt.2016.03.023</a>","ieee":"J. Klüners and F. Nicolae, “Are number fields determined by Artin L-functions?,” <i>Journal of Number Theory</i>, vol. 167, pp. 161–168, 2016, doi: <a href=\"https://doi.org/10.1016/j.jnt.2016.03.023\">10.1016/j.jnt.2016.03.023</a>.","chicago":"Klüners, Jürgen, and Florin Nicolae. “Are Number Fields Determined by Artin L-Functions?” <i>Journal of Number Theory</i> 167 (2016): 161–68. <a href=\"https://doi.org/10.1016/j.jnt.2016.03.023\">https://doi.org/10.1016/j.jnt.2016.03.023</a>.","apa":"Klüners, J., &#38; Nicolae, F. (2016). Are number fields determined by Artin L-functions? <i>Journal of Number Theory</i>, <i>167</i>, 161–168. <a href=\"https://doi.org/10.1016/j.jnt.2016.03.023\">https://doi.org/10.1016/j.jnt.2016.03.023</a>","bibtex":"@article{Klüners_Nicolae_2016, title={Are number fields determined by Artin L-functions?}, volume={167}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2016.03.023\">10.1016/j.jnt.2016.03.023</a>}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Klüners, Jürgen and Nicolae, Florin}, year={2016}, pages={161–168} }","short":"J. Klüners, F. Nicolae, Journal of Number Theory 167 (2016) 161–168.","mla":"Klüners, Jürgen, and Florin Nicolae. “Are Number Fields Determined by Artin L-Functions?” <i>Journal of Number Theory</i>, vol. 167, Elsevier BV, 2016, pp. 161–68, doi:<a href=\"https://doi.org/10.1016/j.jnt.2016.03.023\">10.1016/j.jnt.2016.03.023</a>."},"intvolume":"       167","page":"161-168","_id":"34844","user_id":"93826","department":[{"_id":"102"}],"type":"journal_article","status":"public"},{"language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"publication":"Journal of Number Theory","abstract":[{"text":"We enumerate all positive definite ternary quadratic forms over number fields with class number at most 2. This is done by constructing all definite quaternion orders of type number at most 2 over number fields. Finally, we list all definite quaternion orders of ideal class number 1 or 2.","lang":"eng"}],"date_created":"2023-03-07T08:28:46Z","publisher":"Elsevier BV","title":"Ternary quadratic forms over number fields with small class number","year":"2016","user_id":"93826","department":[{"_id":"102"}],"_id":"42792","extern":"1","type":"journal_article","status":"public","author":[{"last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus","first_name":"Markus"},{"first_name":"David","full_name":"Lorch, David","last_name":"Lorch"}],"volume":161,"date_updated":"2023-04-04T09:10:42Z","doi":"10.1016/j.jnt.2014.11.001","publication_status":"published","publication_identifier":{"issn":["0022-314X"]},"citation":{"short":"M. Kirschmer, D. Lorch, Journal of Number Theory 161 (2016) 343–361.","bibtex":"@article{Kirschmer_Lorch_2016, title={Ternary quadratic forms over number fields with small class number}, volume={161}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2014.11.001\">10.1016/j.jnt.2014.11.001</a>}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer, Markus and Lorch, David}, year={2016}, pages={343–361} }","mla":"Kirschmer, Markus, and David Lorch. “Ternary Quadratic Forms over Number Fields with Small Class Number.” <i>Journal of Number Theory</i>, vol. 161, Elsevier BV, 2016, pp. 343–61, doi:<a href=\"https://doi.org/10.1016/j.jnt.2014.11.001\">10.1016/j.jnt.2014.11.001</a>.","apa":"Kirschmer, M., &#38; Lorch, D. (2016). Ternary quadratic forms over number fields with small class number. <i>Journal of Number Theory</i>, <i>161</i>, 343–361. <a href=\"https://doi.org/10.1016/j.jnt.2014.11.001\">https://doi.org/10.1016/j.jnt.2014.11.001</a>","ama":"Kirschmer M, Lorch D. Ternary quadratic forms over number fields with small class number. <i>Journal of Number Theory</i>. 2016;161:343-361. doi:<a href=\"https://doi.org/10.1016/j.jnt.2014.11.001\">10.1016/j.jnt.2014.11.001</a>","chicago":"Kirschmer, Markus, and David Lorch. “Ternary Quadratic Forms over Number Fields with Small Class Number.” <i>Journal of Number Theory</i> 161 (2016): 343–61. <a href=\"https://doi.org/10.1016/j.jnt.2014.11.001\">https://doi.org/10.1016/j.jnt.2014.11.001</a>.","ieee":"M. Kirschmer and D. Lorch, “Ternary quadratic forms over number fields with small class number,” <i>Journal of Number Theory</i>, vol. 161, pp. 343–361, 2016, doi: <a href=\"https://doi.org/10.1016/j.jnt.2014.11.001\">10.1016/j.jnt.2014.11.001</a>."},"page":"343-361","intvolume":"       161"},{"status":"public","abstract":[{"lang":"eng","text":"Die Gitter von Klassenzahl eins oder zwei sind hier verfügbar: http://www.math.rwth-aachen.de/~Markus.Kirschmer/forms/"}],"type":"misc","extern":"1","language":[{"iso":"eng"}],"department":[{"_id":"102"}],"user_id":"93826","_id":"43454","page":"166","citation":{"apa":"Kirschmer, M. (2016). <i>Definite quadratic and hermitian forms with small class number (Habilitation)</i>.","bibtex":"@book{Kirschmer_2016, place={RWTH Aachen University}, title={Definite quadratic and hermitian forms with small class number (Habilitation)}, author={Kirschmer, Markus}, year={2016} }","short":"M. Kirschmer, Definite Quadratic and Hermitian Forms with Small Class Number (Habilitation), RWTH Aachen University, 2016.","mla":"Kirschmer, Markus. <i>Definite Quadratic and Hermitian Forms with Small Class Number (Habilitation)</i>. 2016.","ama":"Kirschmer M. <i>Definite Quadratic and Hermitian Forms with Small Class Number (Habilitation)</i>.; 2016.","ieee":"M. Kirschmer, <i>Definite quadratic and hermitian forms with small class number (Habilitation)</i>. RWTH Aachen University, 2016.","chicago":"Kirschmer, Markus. <i>Definite Quadratic and Hermitian Forms with Small Class Number (Habilitation)</i>. RWTH Aachen University, 2016."},"place":"RWTH Aachen University","year":"2016","title":"Definite quadratic and hermitian forms with small class number (Habilitation)","date_created":"2023-04-11T08:06:35Z","author":[{"first_name":"Markus","id":"82258","full_name":"Kirschmer, Markus","last_name":"Kirschmer"}],"date_updated":"2023-04-11T08:11:20Z"},{"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","language":[{"iso":"eng"}],"keyword":["Computational Theory and Mathematics","General Mathematics"],"external_id":{"arxiv":["1211.3588"]},"year":"2014","issue":"1","title":"Computation of Galois groups of rational polynomials","date_created":"2022-12-22T10:53:44Z","publisher":"Wiley","status":"public","type":"journal_article","department":[{"_id":"102"}],"user_id":"93826","_id":"34845","page":"141-158","intvolume":"        17","citation":{"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>","short":"C. Fieker, J. Klüners, LMS Journal of Computation and Mathematics 17 (2014) 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>.","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} }","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>.","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>.","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>"},"publication_identifier":{"issn":["1461-1570"]},"publication_status":"published","doi":"10.1112/s1461157013000302","volume":17,"author":[{"first_name":"Claus","full_name":"Fieker, Claus","last_name":"Fieker"},{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"}],"date_updated":"2023-03-06T09:43:56Z"},{"doi":"10.1016/j.jnt.2013.10.007","volume":136,"author":[{"last_name":"Kirschmer","full_name":"Kirschmer, Markus","id":"82258","first_name":"Markus"}],"date_updated":"2023-04-04T09:13:29Z","intvolume":"       136","page":"375-393","citation":{"ieee":"M. Kirschmer, “One-class genera of maximal integral quadratic forms,” <i>Journal of Number Theory</i>, vol. 136, pp. 375–393, 2014, doi: <a href=\"https://doi.org/10.1016/j.jnt.2013.10.007\">10.1016/j.jnt.2013.10.007</a>.","chicago":"Kirschmer, Markus. “One-Class Genera of Maximal Integral Quadratic Forms.” <i>Journal of Number Theory</i> 136 (2014): 375–93. <a href=\"https://doi.org/10.1016/j.jnt.2013.10.007\">https://doi.org/10.1016/j.jnt.2013.10.007</a>.","ama":"Kirschmer M. One-class genera of maximal integral quadratic forms. <i>Journal of Number Theory</i>. 2014;136:375-393. doi:<a href=\"https://doi.org/10.1016/j.jnt.2013.10.007\">10.1016/j.jnt.2013.10.007</a>","bibtex":"@article{Kirschmer_2014, title={One-class genera of maximal integral quadratic forms}, volume={136}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2013.10.007\">10.1016/j.jnt.2013.10.007</a>}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer, Markus}, year={2014}, pages={375–393} }","mla":"Kirschmer, Markus. “One-Class Genera of Maximal Integral Quadratic Forms.” <i>Journal of Number Theory</i>, vol. 136, Elsevier BV, 2014, pp. 375–93, doi:<a href=\"https://doi.org/10.1016/j.jnt.2013.10.007\">10.1016/j.jnt.2013.10.007</a>.","short":"M. Kirschmer, Journal of Number Theory 136 (2014) 375–393.","apa":"Kirschmer, M. (2014). One-class genera of maximal integral quadratic forms. <i>Journal of Number Theory</i>, <i>136</i>, 375–393. <a href=\"https://doi.org/10.1016/j.jnt.2013.10.007\">https://doi.org/10.1016/j.jnt.2013.10.007</a>"},"publication_identifier":{"issn":["0022-314X"]},"publication_status":"published","extern":"1","department":[{"_id":"102"}],"user_id":"93826","_id":"42793","status":"public","type":"journal_article","title":"One-class genera of maximal integral quadratic forms","date_created":"2023-03-07T08:29:34Z","publisher":"Elsevier BV","year":"2014","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"abstract":[{"lang":"eng","text":"Suppose Q is a definite quadratic form on a vector space V over some totally real field K ≠ Q. Then the maximal integral Zₖ-lattices in (V,Q) are locally isometric everywhere and hence form a single genus. We enumerate all orthogonal spaces (V,Q) of dimension at least 3, where the corresponding genus of maximal integral lattices consists of a single isometry class. It turns out, there are 471 such genera. Moreover, the dimension of V and the degree of K are bounded by 6 and 5 respectively. This classification also yields all maximal quaternion orders of type number one."}],"publication":"Journal of Number Theory"},{"date_created":"2023-03-07T08:47:42Z","publisher":"Cambridge University Press (CUP)","title":"Computing with subgroups of the modular group ","issue":"1","year":"2014","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"publication":"Glasgow Mathematical Journal","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."}],"volume":57,"author":[{"id":"82258","full_name":"Kirschmer, Markus","last_name":"Kirschmer","first_name":"Markus"},{"full_name":"LEEDHAM-GREEN, CHARLES","last_name":"LEEDHAM-GREEN","first_name":"CHARLES"}],"date_updated":"2023-04-04T07:55:16Z","doi":"10.1017/s0017089514000202","publication_identifier":{"issn":["0017-0895","1469-509X"]},"publication_status":"published","intvolume":"        57","page":"173-180","citation":{"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>","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>.","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} }","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>.","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>.","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>"},"department":[{"_id":"102"}],"user_id":"93826","_id":"42801","extern":"1","type":"journal_article","status":"public"},{"type":"journal_article","status":"public","department":[{"_id":"102"}],"user_id":"93826","_id":"42794","extern":"1","publication_identifier":{"issn":["1461-1570"]},"publication_status":"published","page":"345-359","intvolume":"        17","citation":{"short":"B. Eick, M. Kirschmer, C. Leedham-Green, LMS Journal of Computation and Mathematics 17 (2014) 345–359.","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>.","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>.","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>.","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>"},"volume":17,"author":[{"full_name":"Eick, B.","last_name":"Eick","first_name":"B."},{"last_name":"Kirschmer","full_name":"Kirschmer, Markus","id":"82258","first_name":"Markus"},{"last_name":"Leedham-Green","full_name":"Leedham-Green, C.","first_name":"C."}],"date_updated":"2023-04-04T09:31:17Z","doi":"10.1112/s1461157014000047","publication":"LMS Journal of Computation and Mathematics","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"}],"language":[{"iso":"eng"}],"keyword":["Computational Theory and Mathematics","General Mathematics"],"issue":"1","year":"2014","date_created":"2023-03-07T08:30:15Z","publisher":"Wiley","title":"The constructive membership problem for discrete free subgroups of rank 2 of SL₂(R)"}]