[{"volume":10,"author":[{"first_name":"Markus","last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus"},{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"}],"date_updated":"2024-11-05T09:46:04Z","doi":"10.1007/s40993-024-00579-6","publication_identifier":{"issn":["2522-0160","2363-9555"]},"publication_status":"published","intvolume":"        10","citation":{"ama":"Kirschmer M, Klüners J. Chow groups of one-dimensional noetherian domains. <i>Research in Number Theory</i>. 2024;10(4). doi:<a href=\"https://doi.org/10.1007/s40993-024-00579-6\">10.1007/s40993-024-00579-6</a>","chicago":"Kirschmer, Markus, and Jürgen Klüners. “Chow Groups of One-Dimensional Noetherian Domains.” <i>Research in Number Theory</i> 10, no. 4 (2024). <a href=\"https://doi.org/10.1007/s40993-024-00579-6\">https://doi.org/10.1007/s40993-024-00579-6</a>.","ieee":"M. Kirschmer and J. Klüners, “Chow groups of one-dimensional noetherian domains,” <i>Research in Number Theory</i>, vol. 10, no. 4, Art. no. 89, 2024, doi: <a href=\"https://doi.org/10.1007/s40993-024-00579-6\">10.1007/s40993-024-00579-6</a>.","apa":"Kirschmer, M., &#38; Klüners, J. (2024). Chow groups of one-dimensional noetherian domains. <i>Research in Number Theory</i>, <i>10</i>(4), Article 89. <a href=\"https://doi.org/10.1007/s40993-024-00579-6\">https://doi.org/10.1007/s40993-024-00579-6</a>","mla":"Kirschmer, Markus, and Jürgen Klüners. “Chow Groups of One-Dimensional Noetherian Domains.” <i>Research in Number Theory</i>, vol. 10, no. 4, 89, Springer Science and Business Media LLC, 2024, doi:<a href=\"https://doi.org/10.1007/s40993-024-00579-6\">10.1007/s40993-024-00579-6</a>.","short":"M. Kirschmer, J. Klüners, Research in Number Theory 10 (2024).","bibtex":"@article{Kirschmer_Klüners_2024, title={Chow groups of one-dimensional noetherian domains}, volume={10}, DOI={<a href=\"https://doi.org/10.1007/s40993-024-00579-6\">10.1007/s40993-024-00579-6</a>}, number={489}, journal={Research in Number Theory}, publisher={Springer Science and Business Media LLC}, author={Kirschmer, Markus and Klüners, Jürgen}, year={2024} }"},"user_id":"82981","_id":"55554","article_number":"89","type":"journal_article","status":"public","date_created":"2024-08-06T07:03:20Z","publisher":"Springer Science and Business Media LLC","title":"Chow groups of one-dimensional noetherian domains","issue":"4","year":"2024","external_id":{"arxiv":["2208.14688"]},"language":[{"iso":"eng"}],"publication":"Research in Number Theory","abstract":[{"text":"We discuss various connections between ideal classes, divisors, Picard and\r\nChow groups of one-dimensional noetherian domains. As a result of these, we\r\ngive a method to compute Chow groups of orders in global fields and show that\r\nthere are infinitely many number fields which contain orders with trivial Chow\r\ngroups.","lang":"eng"}]},{"citation":{"bibtex":"@article{Kirschmer_Nebe_2022, title={Binary Hermitian Lattices over Number Fields}, volume={31}, DOI={<a href=\"https://doi.org/10.1080/10586458.2019.1618756\">10.1080/10586458.2019.1618756</a>}, number={1}, journal={Experimental Mathematics}, publisher={Informa UK Limited}, author={Kirschmer, Markus and Nebe, Gabriele}, year={2022}, pages={280–301} }","short":"M. Kirschmer, G. Nebe, Experimental Mathematics 31 (2022) 280–301.","mla":"Kirschmer, Markus, and Gabriele Nebe. “Binary Hermitian Lattices over Number Fields.” <i>Experimental Mathematics</i>, vol. 31, no. 1, Informa UK Limited, 2022, pp. 280–301, doi:<a href=\"https://doi.org/10.1080/10586458.2019.1618756\">10.1080/10586458.2019.1618756</a>.","apa":"Kirschmer, M., &#38; Nebe, G. (2022). Binary Hermitian Lattices over Number Fields. <i>Experimental Mathematics</i>, <i>31</i>(1), 280–301. <a href=\"https://doi.org/10.1080/10586458.2019.1618756\">https://doi.org/10.1080/10586458.2019.1618756</a>","chicago":"Kirschmer, Markus, and Gabriele Nebe. “Binary Hermitian Lattices over Number Fields.” <i>Experimental Mathematics</i> 31, no. 1 (2022): 280–301. <a href=\"https://doi.org/10.1080/10586458.2019.1618756\">https://doi.org/10.1080/10586458.2019.1618756</a>.","ieee":"M. Kirschmer and G. Nebe, “Binary Hermitian Lattices over Number Fields,” <i>Experimental Mathematics</i>, vol. 31, no. 1, pp. 280–301, 2022, doi: <a href=\"https://doi.org/10.1080/10586458.2019.1618756\">10.1080/10586458.2019.1618756</a>.","ama":"Kirschmer M, Nebe G. Binary Hermitian Lattices over Number Fields. <i>Experimental Mathematics</i>. 2022;31(1):280-301. doi:<a href=\"https://doi.org/10.1080/10586458.2019.1618756\">10.1080/10586458.2019.1618756</a>"},"page":"280-301","intvolume":"        31","year":"2022","issue":"1","publication_status":"published","publication_identifier":{"issn":["1058-6458","1944-950X"]},"doi":"10.1080/10586458.2019.1618756","title":"Binary Hermitian Lattices over Number Fields","author":[{"full_name":"Kirschmer, Markus","id":"82258","last_name":"Kirschmer","first_name":"Markus"},{"first_name":"Gabriele","last_name":"Nebe","full_name":"Nebe, Gabriele"}],"date_created":"2023-07-04T08:28:04Z","volume":31,"date_updated":"2023-07-04T08:29:22Z","publisher":"Informa UK Limited","status":"public","abstract":[{"lang":"eng","text":"In a previous paper the authors developed an algorithm to classify certain quaternary quadratic lattices over totally real fields. The present article applies this algorithm to the classification of binary Hermitian lattices over totally imaginary fields. We use it in particular to classify the 48-dimensional extremal even unimodular lattices over the integers that admit a semilarge automorphism."}],"type":"journal_article","publication":"Experimental Mathematics","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"user_id":"93826","department":[{"_id":"102"}],"_id":"45854"},{"publisher":"American Mathematical Society (AMS)","date_updated":"2023-04-04T07:52:43Z","author":[{"first_name":"Markus","last_name":"Kirschmer","full_name":"Kirschmer, Markus","id":"82258"},{"first_name":"Fabien","full_name":"Narbonne, Fabien","last_name":"Narbonne"},{"first_name":"Christophe","full_name":"Ritzenthaler, Christophe","last_name":"Ritzenthaler"},{"last_name":"Robert","full_name":"Robert, Damien","first_name":"Damien"}],"date_created":"2022-12-23T11:02:02Z","volume":91,"title":"Spanning the isogeny class of a power of an elliptic curve","doi":"10.1090/mcom/3672","publication_status":"published","publication_identifier":{"issn":["0025-5718","1088-6842"]},"issue":"333","year":"2021","citation":{"ieee":"M. Kirschmer, F. Narbonne, C. Ritzenthaler, and D. Robert, “Spanning the isogeny class of a power of an elliptic curve,” <i>Mathematics of Computation</i>, vol. 91, no. 333, pp. 401–449, 2021, doi: <a href=\"https://doi.org/10.1090/mcom/3672\">10.1090/mcom/3672</a>.","chicago":"Kirschmer, Markus, Fabien Narbonne, Christophe Ritzenthaler, and Damien Robert. “Spanning the Isogeny Class of a Power of an Elliptic Curve.” <i>Mathematics of Computation</i> 91, no. 333 (2021): 401–49. <a href=\"https://doi.org/10.1090/mcom/3672\">https://doi.org/10.1090/mcom/3672</a>.","ama":"Kirschmer M, Narbonne F, Ritzenthaler C, Robert D. Spanning the isogeny class of a power of an elliptic curve. <i>Mathematics of Computation</i>. 2021;91(333):401-449. doi:<a href=\"https://doi.org/10.1090/mcom/3672\">10.1090/mcom/3672</a>","short":"M. Kirschmer, F. Narbonne, C. Ritzenthaler, D. Robert, Mathematics of Computation 91 (2021) 401–449.","bibtex":"@article{Kirschmer_Narbonne_Ritzenthaler_Robert_2021, title={Spanning the isogeny class of a power of an elliptic curve}, volume={91}, DOI={<a href=\"https://doi.org/10.1090/mcom/3672\">10.1090/mcom/3672</a>}, number={333}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Kirschmer, Markus and Narbonne, Fabien and Ritzenthaler, Christophe and Robert, Damien}, year={2021}, pages={401–449} }","mla":"Kirschmer, Markus, et al. “Spanning the Isogeny Class of a Power of an Elliptic Curve.” <i>Mathematics of Computation</i>, vol. 91, no. 333, American Mathematical Society (AMS), 2021, pp. 401–49, doi:<a href=\"https://doi.org/10.1090/mcom/3672\">10.1090/mcom/3672</a>.","apa":"Kirschmer, M., Narbonne, F., Ritzenthaler, C., &#38; Robert, D. (2021). Spanning the isogeny class of a power of an elliptic curve. <i>Mathematics of Computation</i>, <i>91</i>(333), 401–449. <a href=\"https://doi.org/10.1090/mcom/3672\">https://doi.org/10.1090/mcom/3672</a>"},"intvolume":"        91","page":"401-449","_id":"34912","user_id":"93826","department":[{"_id":"102"}],"keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Mathematics of Computation","abstract":[{"text":"Let E be an ordinary elliptic curve over a finite field and g be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class of E⁹ . The varieties are first described as hermitian lattices over (not necessarily maximal) quadratic orders and then geometrically in terms of their algebraic theta null point. We also show how to algebraically compute Siegel modular forms of even weight given as polynomials in the theta constants by a careful choice of an affine lift of the theta null point. We then use these results to give an algebraic computation of Serre’s obstruction for principally polarized abelian threefolds isogenous to E³ and of the Igusa modular form in dimension 4. We illustrate our algorithms with examples of curves with many rational points over finite fields. ","lang":"eng"}],"status":"public"},{"type":"journal_article","publication":"International Journal of Number Theory","abstract":[{"text":"We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of (V,q). This yields a good algorithm to enumerate a system of representatives of proper isometry classes of lattices in genera of maximal lattices in (V,q).","lang":"eng"}],"status":"public","_id":"34917","user_id":"82258","department":[{"_id":"102"}],"keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1793-0421","1793-7310"]},"issue":"02","year":"2019","citation":{"apa":"Kirschmer, M., &#38; Nebe, G. (2019). Quaternary quadratic lattices over number fields. <i>International Journal of Number Theory</i>, <i>15</i>(02), 309–325. <a href=\"https://doi.org/10.1142/s1793042119500131\">https://doi.org/10.1142/s1793042119500131</a>","mla":"Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over Number Fields.” <i>International Journal of Number Theory</i>, vol. 15, no. 02, World Scientific Pub Co Pte Lt, 2019, pp. 309–25, doi:<a href=\"https://doi.org/10.1142/s1793042119500131\">10.1142/s1793042119500131</a>.","bibtex":"@article{Kirschmer_Nebe_2019, title={Quaternary quadratic lattices over number fields}, volume={15}, DOI={<a href=\"https://doi.org/10.1142/s1793042119500131\">10.1142/s1793042119500131</a>}, number={02}, journal={International Journal of Number Theory}, publisher={World Scientific Pub Co Pte Lt}, author={Kirschmer, Markus and Nebe, Gabriele}, year={2019}, pages={309–325} }","short":"M. Kirschmer, G. Nebe, International Journal of Number Theory 15 (2019) 309–325.","chicago":"Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over Number Fields.” <i>International Journal of Number Theory</i> 15, no. 02 (2019): 309–25. <a href=\"https://doi.org/10.1142/s1793042119500131\">https://doi.org/10.1142/s1793042119500131</a>.","ieee":"M. Kirschmer and G. Nebe, “Quaternary quadratic lattices over number fields,” <i>International Journal of Number Theory</i>, vol. 15, no. 02, pp. 309–325, 2019, doi: <a href=\"https://doi.org/10.1142/s1793042119500131\">10.1142/s1793042119500131</a>.","ama":"Kirschmer M, Nebe G. Quaternary quadratic lattices over number fields. <i>International Journal of Number Theory</i>. 2019;15(02):309-325. doi:<a href=\"https://doi.org/10.1142/s1793042119500131\">10.1142/s1793042119500131</a>"},"intvolume":"        15","page":"309-325","publisher":"World Scientific Pub Co Pte Lt","date_updated":"2023-12-06T10:05:59Z","date_created":"2022-12-23T11:05:09Z","author":[{"last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus","first_name":"Markus"},{"first_name":"Gabriele","full_name":"Nebe, Gabriele","last_name":"Nebe"}],"volume":15,"title":"Quaternary quadratic lattices over number fields","doi":"10.1142/s1793042119500131"},{"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","publication":"Journal of Number Theory","type":"journal_article","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"_id":"34916","department":[{"_id":"102"}],"user_id":"82258","year":"2019","page":"121-134","intvolume":"       197","citation":{"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>.","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>.","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>","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>.","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} }","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>"},"publication_identifier":{"issn":["0022-314X"]},"publication_status":"published","title":"Automorphisms of even unimodular lattices over number fields","doi":"10.1016/j.jnt.2018.08.004","date_updated":"2023-12-06T10:07:17Z","publisher":"Elsevier BV","volume":197,"author":[{"last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus","first_name":"Markus"}],"date_created":"2022-12-23T11:04:34Z"},{"volume":113,"author":[{"id":"82258","full_name":"Kirschmer, Markus","last_name":"Kirschmer","first_name":"Markus"}],"date_updated":"2023-04-04T09:05:04Z","doi":"10.1007/s00013-019-01348-z","publication_identifier":{"issn":["0003-889X","1420-8938"]},"publication_status":"published","page":"337-347","intvolume":"       113","citation":{"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} }","short":"M. Kirschmer, Archiv Der Mathematik 113 (2019) 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>.","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>","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>.","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>.","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>"},"department":[{"_id":"102"}],"user_id":"93826","_id":"34915","type":"journal_article","status":"public","date_created":"2022-12-23T11:03:41Z","publisher":"Springer Science and Business Media LLC","title":"Determinant groups of Hermitian lattices over local fields","issue":"4","year":"2019","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"publication":"Archiv der Mathematik","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"}]},{"title":"One Class Genera of Lattice Chains Over Number Fields","doi":"10.1007/978-3-319-70566-8_22","date_updated":"2023-04-04T09:08:19Z","publisher":"Springer International Publishing","author":[{"last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus","first_name":"Markus"},{"first_name":"Gabriele","full_name":"Nebe, Gabriele","last_name":"Nebe"}],"date_created":"2023-03-07T08:23:48Z","place":"Cham","year":"2018","citation":{"short":"M. Kirschmer, G. Nebe, in: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, Springer International Publishing, Cham, 2018.","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} }","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>.","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>","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."},"publication_status":"published","publication_identifier":{"isbn":["9783319705651","9783319705668"]},"language":[{"iso":"eng"}],"extern":"1","_id":"42788","user_id":"93826","department":[{"_id":"102"}],"abstract":[{"lang":"eng","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."}],"status":"public","type":"book_chapter","publication":"Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory"},{"language":[{"iso":"eng"}],"extern":"1","keyword":["Algebra and Number Theory"],"department":[{"_id":"102"}],"user_id":"93826","_id":"42790","status":"public","abstract":[{"lang":"eng","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."}],"publication":"Journal de Théorie des Nombres de Bordeaux","type":"journal_article","doi":"10.5802/jtnb.1052","title":"One-class genera of exceptional groups over number fields","volume":30,"date_created":"2023-03-07T08:27:36Z","author":[{"id":"82258","full_name":"Kirschmer, Markus","last_name":"Kirschmer","first_name":"Markus"}],"publisher":"Cellule MathDoc/CEDRAM","date_updated":"2023-04-04T09:07:32Z","page":"847-857","intvolume":"        30","citation":{"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>.","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>.","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>.","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>"},"year":"2018","issue":"3","publication_identifier":{"issn":["1246-7405","2118-8572"]},"publication_status":"published"},{"extern":"1","user_id":"93826","department":[{"_id":"102"}],"_id":"42791","status":"public","type":"journal_article","doi":"10.1016/j.jalgebra.2017.02.029","author":[{"first_name":"Markus","last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus"},{"last_name":"Rüther","full_name":"Rüther, Marion G.","first_name":"Marion G."}],"volume":480,"date_updated":"2023-04-04T09:10:14Z","citation":{"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>","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>.","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."},"page":"519-548","intvolume":"       480","publication_status":"published","publication_identifier":{"issn":["0021-8693"]},"language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"abstract":[{"lang":"eng","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."}],"publication":"Journal of Algebra","title":"The constructive membership problem for discrete two-generator subgroups of SL(2,R)","date_created":"2023-03-07T08:28:11Z","publisher":"Elsevier BV","year":"2017"},{"extern":"1","_id":"42792","department":[{"_id":"102"}],"user_id":"93826","status":"public","type":"journal_article","doi":"10.1016/j.jnt.2014.11.001","date_updated":"2023-04-04T09:10:42Z","volume":161,"author":[{"full_name":"Kirschmer, Markus","id":"82258","last_name":"Kirschmer","first_name":"Markus"},{"first_name":"David","last_name":"Lorch","full_name":"Lorch, David"}],"page":"343-361","intvolume":"       161","citation":{"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>","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} }","short":"M. Kirschmer, D. Lorch, Journal of Number Theory 161 (2016) 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>.","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>."},"publication_identifier":{"issn":["0022-314X"]},"publication_status":"published","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"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"}],"publication":"Journal of Number Theory","title":"Ternary quadratic forms over number fields with small class number","publisher":"Elsevier BV","date_created":"2023-03-07T08:28:46Z","year":"2016"},{"type":"misc","abstract":[{"text":"Die Gitter von Klassenzahl eins oder zwei sind hier verfügbar: http://www.math.rwth-aachen.de/~Markus.Kirschmer/forms/","lang":"eng"}],"status":"public","_id":"43454","user_id":"93826","department":[{"_id":"102"}],"extern":"1","language":[{"iso":"eng"}],"place":"RWTH Aachen University","year":"2016","citation":{"bibtex":"@book{Kirschmer_2016, place={RWTH Aachen University}, title={Definite quadratic and hermitian forms with small class number (Habilitation)}, author={Kirschmer, Markus}, year={2016} }","mla":"Kirschmer, Markus. <i>Definite Quadratic and Hermitian Forms with Small Class Number (Habilitation)</i>. 2016.","short":"M. Kirschmer, Definite Quadratic and Hermitian Forms with Small Class Number (Habilitation), RWTH Aachen University, 2016.","apa":"Kirschmer, M. (2016). <i>Definite quadratic and hermitian forms with small class number (Habilitation)</i>.","chicago":"Kirschmer, Markus. <i>Definite Quadratic and Hermitian Forms with Small Class Number (Habilitation)</i>. RWTH Aachen University, 2016.","ieee":"M. Kirschmer, <i>Definite quadratic and hermitian forms with small class number (Habilitation)</i>. RWTH Aachen University, 2016.","ama":"Kirschmer M. <i>Definite Quadratic and Hermitian Forms with Small Class Number (Habilitation)</i>.; 2016."},"page":"166","date_updated":"2023-04-11T08:11:20Z","date_created":"2023-04-11T08:06:35Z","author":[{"first_name":"Markus","last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus"}],"title":"Definite quadratic and hermitian forms with small class number (Habilitation)"},{"extern":"1","_id":"42793","user_id":"93826","department":[{"_id":"102"}],"status":"public","type":"journal_article","doi":"10.1016/j.jnt.2013.10.007","date_updated":"2023-04-04T09:13:29Z","author":[{"last_name":"Kirschmer","full_name":"Kirschmer, Markus","id":"82258","first_name":"Markus"}],"volume":136,"citation":{"short":"M. Kirschmer, Journal of Number Theory 136 (2014) 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>.","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} }","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>","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>.","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>.","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>"},"intvolume":"       136","page":"375-393","publication_status":"published","publication_identifier":{"issn":["0022-314X"]},"keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"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","title":"One-class genera of maximal integral quadratic forms","publisher":"Elsevier BV","date_created":"2023-03-07T08:29:34Z","year":"2014"},{"title":"Computing with subgroups of the modular group ","date_created":"2023-03-07T08:47:42Z","publisher":"Cambridge University Press (CUP)","year":"2014","issue":"1","language":[{"iso":"eng"}],"keyword":["General 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"}],"publication":"Glasgow Mathematical Journal","doi":"10.1017/s0017089514000202","author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","id":"82258","last_name":"Kirschmer"},{"first_name":"CHARLES","full_name":"LEEDHAM-GREEN, CHARLES","last_name":"LEEDHAM-GREEN"}],"volume":57,"date_updated":"2023-04-04T07:55:16Z","citation":{"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>","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>.","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.","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>.","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>"},"intvolume":"        57","page":"173-180","publication_status":"published","publication_identifier":{"issn":["0017-0895","1469-509X"]},"extern":"1","user_id":"93826","department":[{"_id":"102"}],"_id":"42801","status":"public","type":"journal_article"},{"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."}],"publication":"LMS Journal of Computation and Mathematics","keyword":["Computational Theory and Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"year":"2014","issue":"1","title":"The constructive membership problem for discrete free subgroups of rank 2 of SL₂(R)","publisher":"Wiley","date_created":"2023-03-07T08:30:15Z","status":"public","type":"journal_article","extern":"1","_id":"42794","user_id":"93826","department":[{"_id":"102"}],"citation":{"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>","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} }","short":"B. Eick, M. Kirschmer, C. Leedham-Green, LMS Journal of Computation and Mathematics 17 (2014) 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>.","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>"},"page":"345-359","intvolume":"        17","publication_status":"published","publication_identifier":{"issn":["1461-1570"]},"doi":"10.1112/s1461157014000047","date_updated":"2023-04-04T09:31:17Z","author":[{"first_name":"B.","full_name":"Eick, B.","last_name":"Eick"},{"last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus","first_name":"Markus"},{"full_name":"Leedham-Green, C.","last_name":"Leedham-Green","first_name":"C."}],"volume":17},{"year":"2013","citation":{"apa":"Kirschmer, M., &#38; Mertens, M. H. (2013). On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves. In <i>Integers</i>. DE GRUYTER. <a href=\"https://doi.org/10.1515/9783110298161.212\">https://doi.org/10.1515/9783110298161.212</a>","mla":"Kirschmer, Markus, and Michael H. Mertens. “On an Analogue to the Lucas-Lehmer-Riesel Test Using Elliptic Curves.” <i>Integers</i>, DE GRUYTER, 2013, doi:<a href=\"https://doi.org/10.1515/9783110298161.212\">10.1515/9783110298161.212</a>.","bibtex":"@inbook{Kirschmer_Mertens_2013, title={On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves}, DOI={<a href=\"https://doi.org/10.1515/9783110298161.212\">10.1515/9783110298161.212</a>}, booktitle={Integers}, publisher={DE GRUYTER}, author={Kirschmer, Markus and Mertens, Michael H.}, year={2013} }","short":"M. Kirschmer, M.H. Mertens, in: Integers, DE GRUYTER, 2013.","chicago":"Kirschmer, Markus, and Michael H. Mertens. “On an Analogue to the Lucas-Lehmer-Riesel Test Using Elliptic Curves.” In <i>Integers</i>. DE GRUYTER, 2013. <a href=\"https://doi.org/10.1515/9783110298161.212\">https://doi.org/10.1515/9783110298161.212</a>.","ieee":"M. Kirschmer and M. H. Mertens, “On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves,” in <i>Integers</i>, DE GRUYTER, 2013.","ama":"Kirschmer M, Mertens MH. On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves. In: <i>Integers</i>. DE GRUYTER; 2013. doi:<a href=\"https://doi.org/10.1515/9783110298161.212\">10.1515/9783110298161.212</a>"},"publication_status":"published","publication_identifier":{"isbn":["9783110298116"]},"title":"On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves","doi":"10.1515/9783110298161.212","publisher":"DE GRUYTER","date_updated":"2023-04-04T09:17:32Z","author":[{"first_name":"Markus","last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus"},{"first_name":"Michael H.","full_name":"Mertens, Michael H.","last_name":"Mertens"}],"date_created":"2023-03-07T08:51:46Z","abstract":[{"text":"Following an idea of B. H. Gross, who presented an elliptic curve test for Mersenneprimes Mₚ=2ᵖ−1, we propose a similar test with elliptic curves for generalizedThabit primesK(h, n) := h·2ⁿ−1 for any positive odd number h and any integer n> log₂(h)+2.","lang":"eng"}],"status":"public","type":"book_chapter","publication":"Integers","extern":"1","language":[{"iso":"eng"}],"_id":"42805","user_id":"93826","department":[{"_id":"102"}]},{"language":[{"iso":"eng"}],"keyword":["Computational Theory and Mathematics","General Mathematics"],"abstract":[{"lang":"eng","text":"We give an enumeration of all positive definite primitive Z-lattices in dimension n ≥ 3 whose genus consists of a single isometry class. This is achieved by using bounds obtained from the Smith–Minkowski–Siegel mass formula to computationally construct the square-free determinant lattices with this property, and then repeatedly calculating pre-images under a mapping first introduced by G. L. Watson.\r\n\r\nWe hereby complete the classification of single-class genera in dimensions 4 and 5 and correct some mistakes in Watson’s classifications in other dimensions. A list of all single-class primitive Z-lattices has been compiled and incorporated into the Catalogue of Lattices."}],"publication":"LMS Journal of Computation and Mathematics","title":"Single-class genera of positive integral lattices","date_created":"2023-03-07T08:34:28Z","publisher":"Wiley","year":"2013","extern":"1","department":[{"_id":"102"}],"user_id":"93826","_id":"42796","status":"public","type":"journal_article","doi":"10.1112/s1461157013000107","volume":16,"author":[{"first_name":"David","last_name":"Lorch","full_name":"Lorch, David"},{"id":"82258","full_name":"Kirschmer, Markus","last_name":"Kirschmer","first_name":"Markus"}],"date_updated":"2023-04-04T07:57:04Z","page":"172-186","intvolume":"        16","citation":{"mla":"Lorch, David, and Markus Kirschmer. “Single-Class Genera of Positive Integral Lattices.” <i>LMS Journal of Computation and Mathematics</i>, vol. 16, Wiley, 2013, pp. 172–86, doi:<a href=\"https://doi.org/10.1112/s1461157013000107\">10.1112/s1461157013000107</a>.","bibtex":"@article{Lorch_Kirschmer_2013, title={Single-class genera of positive integral lattices}, volume={16}, DOI={<a href=\"https://doi.org/10.1112/s1461157013000107\">10.1112/s1461157013000107</a>}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Lorch, David and Kirschmer, Markus}, year={2013}, pages={172–186} }","short":"D. Lorch, M. Kirschmer, LMS Journal of Computation and Mathematics 16 (2013) 172–186.","apa":"Lorch, D., &#38; Kirschmer, M. (2013). Single-class genera of positive integral lattices. <i>LMS Journal of Computation and Mathematics</i>, <i>16</i>, 172–186. <a href=\"https://doi.org/10.1112/s1461157013000107\">https://doi.org/10.1112/s1461157013000107</a>","ieee":"D. Lorch and M. Kirschmer, “Single-class genera of positive integral lattices,” <i>LMS Journal of Computation and Mathematics</i>, vol. 16, pp. 172–186, 2013, doi: <a href=\"https://doi.org/10.1112/s1461157013000107\">10.1112/s1461157013000107</a>.","chicago":"Lorch, David, and Markus Kirschmer. “Single-Class Genera of Positive Integral Lattices.” <i>LMS Journal of Computation and Mathematics</i> 16 (2013): 172–86. <a href=\"https://doi.org/10.1112/s1461157013000107\">https://doi.org/10.1112/s1461157013000107</a>.","ama":"Lorch D, Kirschmer M. Single-class genera of positive integral lattices. <i>LMS Journal of Computation and Mathematics</i>. 2013;16:172-186. doi:<a href=\"https://doi.org/10.1112/s1461157013000107\">10.1112/s1461157013000107</a>"},"publication_identifier":{"issn":["1461-1570"]},"publication_status":"published"},{"publication_status":"published","publication_identifier":{"issn":["0025-5718","1088-6842"]},"issue":"279","year":"2012","citation":{"ama":"Kirschmer M. A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$. <i>Mathematics of Computation</i>. 2012;81(279):1619-1634. doi:<a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">10.1090/s0025-5718-2011-02570-6</a>","chicago":"Kirschmer, Markus. “A Normal Form for Definite Quadratic Forms over $\\mathbb{F}_{q}[t]$.” <i>Mathematics of Computation</i> 81, no. 279 (2012): 1619–34. <a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">https://doi.org/10.1090/s0025-5718-2011-02570-6</a>.","ieee":"M. Kirschmer, “A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$,” <i>Mathematics of Computation</i>, vol. 81, no. 279, pp. 1619–1634, 2012, doi: <a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">10.1090/s0025-5718-2011-02570-6</a>.","apa":"Kirschmer, M. (2012). A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$. <i>Mathematics of Computation</i>, <i>81</i>(279), 1619–1634. <a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">https://doi.org/10.1090/s0025-5718-2011-02570-6</a>","bibtex":"@article{Kirschmer_2012, title={A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$}, volume={81}, DOI={<a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">10.1090/s0025-5718-2011-02570-6</a>}, number={279}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Kirschmer, Markus}, year={2012}, pages={1619–1634} }","short":"M. Kirschmer, Mathematics of Computation 81 (2012) 1619–1634.","mla":"Kirschmer, Markus. “A Normal Form for Definite Quadratic Forms over $\\mathbb{F}_{q}[t]$.” <i>Mathematics of Computation</i>, vol. 81, no. 279, American Mathematical Society (AMS), 2012, pp. 1619–34, doi:<a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">10.1090/s0025-5718-2011-02570-6</a>."},"page":"1619-1634","intvolume":"        81","date_updated":"2023-04-04T09:22:22Z","publisher":"American Mathematical Society (AMS)","author":[{"last_name":"Kirschmer","full_name":"Kirschmer, Markus","id":"82258","first_name":"Markus"}],"date_created":"2023-03-07T08:35:56Z","volume":81,"title":"A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$","doi":"10.1090/s0025-5718-2011-02570-6","type":"journal_article","publication":"Mathematics of Computation","abstract":[{"text":"An efficient algorithm to compute automorphism groups and isometries of definite Fq[t]-lattices for odd q is presented. The algorithm requires several square root computations in Fq₂ but no enumeration of orbits having more than eight elements. ","lang":"eng"}],"status":"public","_id":"42797","user_id":"93826","department":[{"_id":"102"}],"keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"extern":"1","language":[{"iso":"eng"}]},{"type":"journal_article","publication":"Experimental Mathematics","abstract":[{"lang":"eng","text":"This paper classifies the maximal finite subgroups of SP₂ₙ(Q) for 1⩽n⩽11 up to GL₂ₙ(Q) conjugacy in ."}],"status":"public","_id":"42798","user_id":"93826","department":[{"_id":"102"}],"keyword":["General Mathematics"],"extern":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1058-6458","1944-950X"]},"issue":"2","year":"2011","citation":{"apa":"Kirschmer, M. (2011). Finite Symplectic Matrix Groups. <i>Experimental Mathematics</i>, <i>20</i>(2), 217–228. <a href=\"https://doi.org/10.1080/10586458.2011.564964\">https://doi.org/10.1080/10586458.2011.564964</a>","bibtex":"@article{Kirschmer_2011, title={Finite Symplectic Matrix Groups}, volume={20}, DOI={<a href=\"https://doi.org/10.1080/10586458.2011.564964\">10.1080/10586458.2011.564964</a>}, number={2}, journal={Experimental Mathematics}, publisher={Informa UK Limited}, author={Kirschmer, Markus}, year={2011}, pages={217–228} }","short":"M. Kirschmer, Experimental Mathematics 20 (2011) 217–228.","mla":"Kirschmer, Markus. “Finite Symplectic Matrix Groups.” <i>Experimental Mathematics</i>, vol. 20, no. 2, Informa UK Limited, 2011, pp. 217–28, doi:<a href=\"https://doi.org/10.1080/10586458.2011.564964\">10.1080/10586458.2011.564964</a>.","ama":"Kirschmer M. Finite Symplectic Matrix Groups. <i>Experimental Mathematics</i>. 2011;20(2):217-228. doi:<a href=\"https://doi.org/10.1080/10586458.2011.564964\">10.1080/10586458.2011.564964</a>","ieee":"M. Kirschmer, “Finite Symplectic Matrix Groups,” <i>Experimental Mathematics</i>, vol. 20, no. 2, pp. 217–228, 2011, doi: <a href=\"https://doi.org/10.1080/10586458.2011.564964\">10.1080/10586458.2011.564964</a>.","chicago":"Kirschmer, Markus. “Finite Symplectic Matrix Groups.” <i>Experimental Mathematics</i> 20, no. 2 (2011): 217–28. <a href=\"https://doi.org/10.1080/10586458.2011.564964\">https://doi.org/10.1080/10586458.2011.564964</a>."},"intvolume":"        20","page":"217-228","publisher":"Informa UK Limited","date_updated":"2023-04-04T09:24:42Z","author":[{"last_name":"Kirschmer","full_name":"Kirschmer, Markus","id":"82258","first_name":"Markus"}],"date_created":"2023-03-07T08:36:46Z","volume":20,"title":"Finite Symplectic Matrix Groups","doi":"10.1080/10586458.2011.564964"},{"user_id":"93826","department":[{"_id":"102"}],"_id":"42803","extern":"1","type":"journal_article","status":"public","author":[{"first_name":"Markus","id":"82258","full_name":"Kirschmer, Markus","last_name":"Kirschmer"},{"full_name":"Voight, John","last_name":"Voight","first_name":"John"}],"volume":39,"date_updated":"2023-04-04T09:25:08Z","doi":"10.1137/080734467","publication_status":"published","publication_identifier":{"issn":["0097-5397","1095-7111"]},"citation":{"apa":"Kirschmer, M., &#38; Voight, J. (2010). Algorithmic Enumeration of Ideal Classes for Quaternion Orders. <i>SIAM Journal on Computing</i>, <i>39</i>(5), 1714–1747. <a href=\"https://doi.org/10.1137/080734467\">https://doi.org/10.1137/080734467</a>","short":"M. Kirschmer, J. Voight, SIAM Journal on Computing 39 (2010) 1714–1747.","bibtex":"@article{Kirschmer_Voight_2010, title={Algorithmic Enumeration of Ideal Classes for Quaternion Orders}, volume={39}, DOI={<a href=\"https://doi.org/10.1137/080734467\">10.1137/080734467</a>}, number={5}, journal={SIAM Journal on Computing}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Kirschmer, Markus and Voight, John}, year={2010}, pages={1714–1747} }","mla":"Kirschmer, Markus, and John Voight. “Algorithmic Enumeration of Ideal Classes for Quaternion Orders.” <i>SIAM Journal on Computing</i>, vol. 39, no. 5, Society for Industrial &#38; Applied Mathematics (SIAM), 2010, pp. 1714–47, doi:<a href=\"https://doi.org/10.1137/080734467\">10.1137/080734467</a>.","ama":"Kirschmer M, Voight J. Algorithmic Enumeration of Ideal Classes for Quaternion Orders. <i>SIAM Journal on Computing</i>. 2010;39(5):1714-1747. doi:<a href=\"https://doi.org/10.1137/080734467\">10.1137/080734467</a>","chicago":"Kirschmer, Markus, and John Voight. “Algorithmic Enumeration of Ideal Classes for Quaternion Orders.” <i>SIAM Journal on Computing</i> 39, no. 5 (2010): 1714–47. <a href=\"https://doi.org/10.1137/080734467\">https://doi.org/10.1137/080734467</a>.","ieee":"M. Kirschmer and J. Voight, “Algorithmic Enumeration of Ideal Classes for Quaternion Orders,” <i>SIAM Journal on Computing</i>, vol. 39, no. 5, pp. 1714–1747, 2010, doi: <a href=\"https://doi.org/10.1137/080734467\">10.1137/080734467</a>."},"intvolume":"        39","page":"1714-1747","language":[{"iso":"eng"}],"keyword":["General Mathematics","General Computer Science"],"publication":"SIAM Journal on Computing","abstract":[{"lang":"eng","text":"We provide algorithms to count and enumerate representatives of the (right) ideal classes of an Eichler order in a quaternion algebra defined over a number field. We analyze the run time of these algorithms and consider several related problems, including the computation of two-sided ideal classes, isomorphism classes of orders, connecting ideals for orders, and ideal principalization. We conclude by giving the complete list of definite Eichler orders with class number at most 2."}],"date_created":"2023-03-07T08:49:35Z","publisher":"Society for Industrial & Applied Mathematics (SIAM)","title":"Algorithmic Enumeration of Ideal Classes for Quaternion Orders","issue":"5","year":"2010"},{"_id":"43453","department":[{"_id":"102"}],"user_id":"93826","extern":"1","language":[{"iso":"eng"}],"type":"dissertation","abstract":[{"text":"Die invarianten Formen aus dem Anhang sind hier verfügbar:http://www.math.rwth-aachen.de/homes/Markus.Kirschmer/symplectic/","lang":"eng"}],"status":"public","date_updated":"2023-04-11T08:14:10Z","date_created":"2023-04-11T08:03:29Z","author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","id":"82258","last_name":"Kirschmer"}],"title":"Finite symplectic matrix groups (Dissertation)","year":"2009","place":"RWTH Aachen University","page":"149","citation":{"chicago":"Kirschmer, Markus. <i>Finite Symplectic Matrix Groups (Dissertation)</i>. RWTH Aachen University, 2009.","ieee":"M. Kirschmer, <i>Finite symplectic matrix groups (Dissertation)</i>. RWTH Aachen University, 2009.","ama":"Kirschmer M. <i>Finite Symplectic Matrix Groups (Dissertation)</i>.; 2009.","short":"M. Kirschmer, Finite Symplectic Matrix Groups (Dissertation), RWTH Aachen University, 2009.","mla":"Kirschmer, Markus. <i>Finite Symplectic Matrix Groups (Dissertation)</i>. 2009.","bibtex":"@book{Kirschmer_2009, place={RWTH Aachen University}, title={Finite symplectic matrix groups (Dissertation)}, author={Kirschmer, Markus}, year={2009} }","apa":"Kirschmer, M. (2009). <i>Finite symplectic matrix groups (Dissertation)</i>."}}]