[{"language":[{"iso":"eng"}],"year":"2022","type":"preprint","citation":{"short":"M. Kirschmer, J. Klüners, (2022).","ieee":"M. Kirschmer and J. Klüners, “Chow groups of orders in number fields.” 2022.","chicago":"Kirschmer, Markus, and Jürgen Klüners. “Chow Groups of Orders in Number Fields,” 2022.","apa":"Kirschmer, M., & Klüners, J. (2022). Chow groups of orders in number fields.","ama":"Kirschmer M, Klüners J. Chow groups of orders in number fields. Published online 2022.","bibtex":"@article{Kirschmer_Klüners_2022, title={Chow groups of orders in number fields}, author={Kirschmer, Markus and Klüners, Jürgen }, year={2022} }","mla":"Kirschmer, Markus, and Jürgen Klüners. Chow Groups of Orders in Number Fields. 2022."},"date_updated":"2023-04-04T07:42:56Z","_id":"43392","date_created":"2023-04-04T07:40:58Z","status":"public","department":[{"_id":"102"}],"author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","last_name":"Kirschmer","id":"82258"},{"full_name":"Klüners, Jürgen ","first_name":"Jürgen ","last_name":"Klüners"}],"user_id":"93826","title":"Chow groups of orders in number fields"},{"keyword":["General Mathematics"],"publication":"Experimental Mathematics","publisher":"Informa UK Limited","author":[{"full_name":"Kirschmer, Markus","first_name":"Markus","id":"82258","last_name":"Kirschmer"},{"last_name":"Nebe","full_name":"Nebe, Gabriele","first_name":"Gabriele"}],"date_created":"2023-07-04T08:28:04Z","status":"public","volume":31,"abstract":[{"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.","lang":"eng"}],"user_id":"93826","page":"280-301","citation":{"short":"M. Kirschmer, G. Nebe, Experimental Mathematics 31 (2022) 280–301.","ieee":"M. Kirschmer and G. Nebe, “Binary Hermitian Lattices over Number Fields,” Experimental Mathematics, vol. 31, no. 1, pp. 280–301, 2022, doi: 10.1080/10586458.2019.1618756.","chicago":"Kirschmer, Markus, and Gabriele Nebe. “Binary Hermitian Lattices over Number Fields.” Experimental Mathematics 31, no. 1 (2022): 280–301. https://doi.org/10.1080/10586458.2019.1618756.","apa":"Kirschmer, M., & Nebe, G. (2022). Binary Hermitian Lattices over Number Fields. Experimental Mathematics, 31(1), 280–301. https://doi.org/10.1080/10586458.2019.1618756","ama":"Kirschmer M, Nebe G. Binary Hermitian Lattices over Number Fields. Experimental Mathematics. 2022;31(1):280-301. doi:10.1080/10586458.2019.1618756","bibtex":"@article{Kirschmer_Nebe_2022, title={Binary Hermitian Lattices over Number Fields}, volume={31}, DOI={10.1080/10586458.2019.1618756}, number={1}, journal={Experimental Mathematics}, publisher={Informa UK Limited}, author={Kirschmer, Markus and Nebe, Gabriele}, year={2022}, pages={280–301} }","mla":"Kirschmer, Markus, and Gabriele Nebe. “Binary Hermitian Lattices over Number Fields.” Experimental Mathematics, vol. 31, no. 1, Informa UK Limited, 2022, pp. 280–301, doi:10.1080/10586458.2019.1618756."},"year":"2022","type":"journal_article","_id":"45854","intvolume":" 31","issue":"1","department":[{"_id":"102"}],"publication_status":"published","publication_identifier":{"issn":["1058-6458","1944-950X"]},"title":"Binary Hermitian Lattices over Number Fields","language":[{"iso":"eng"}],"date_updated":"2023-07-04T08:29:22Z","doi":"10.1080/10586458.2019.1618756"},{"publication_identifier":{"issn":["0025-5718","1088-6842"]},"publication_status":"published","department":[{"_id":"102"}],"title":"Spanning the isogeny class of a power of an elliptic curve","language":[{"iso":"eng"}],"doi":"10.1090/mcom/3672","date_updated":"2023-04-04T07:52:43Z","status":"public","date_created":"2022-12-23T11:02:02Z","volume":91,"publisher":"American Mathematical Society (AMS)","author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","last_name":"Kirschmer","id":"82258"},{"full_name":"Narbonne, Fabien","first_name":"Fabien","last_name":"Narbonne"},{"full_name":"Ritzenthaler, Christophe","first_name":"Christophe","last_name":"Ritzenthaler"},{"last_name":"Robert","full_name":"Robert, Damien","first_name":"Damien"}],"keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"publication":"Mathematics of Computation","user_id":"93826","abstract":[{"lang":"eng","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. "}],"type":"journal_article","year":"2021","citation":{"ieee":"M. Kirschmer, F. Narbonne, C. Ritzenthaler, and D. Robert, “Spanning the isogeny class of a power of an elliptic curve,” Mathematics of Computation, vol. 91, no. 333, pp. 401–449, 2021, doi: 10.1090/mcom/3672.","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={10.1090/mcom/3672}, 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.” Mathematics of Computation, vol. 91, no. 333, American Mathematical Society (AMS), 2021, pp. 401–49, doi:10.1090/mcom/3672.","ama":"Kirschmer M, Narbonne F, Ritzenthaler C, Robert D. Spanning the isogeny class of a power of an elliptic curve. Mathematics of Computation. 2021;91(333):401-449. doi:10.1090/mcom/3672","apa":"Kirschmer, M., Narbonne, F., Ritzenthaler, C., & Robert, D. (2021). Spanning the isogeny class of a power of an elliptic curve. Mathematics of Computation, 91(333), 401–449. https://doi.org/10.1090/mcom/3672","chicago":"Kirschmer, Markus, Fabien Narbonne, Christophe Ritzenthaler, and Damien Robert. “Spanning the Isogeny Class of a Power of an Elliptic Curve.” Mathematics of Computation 91, no. 333 (2021): 401–49. https://doi.org/10.1090/mcom/3672."},"page":"401-449","issue":"333","_id":"34912","intvolume":" 91"},{"type":"journal_article","year":"2019","citation":{"apa":"Kirschmer, M. (2019). Determinant groups of Hermitian lattices over local fields. Archiv Der Mathematik, 113(4), 337–347. https://doi.org/10.1007/s00013-019-01348-z","ama":"Kirschmer M. Determinant groups of Hermitian lattices over local fields. Archiv der Mathematik. 2019;113(4):337-347. doi:10.1007/s00013-019-01348-z","chicago":"Kirschmer, Markus. “Determinant Groups of Hermitian Lattices over Local Fields.” Archiv Der Mathematik 113, no. 4 (2019): 337–47. https://doi.org/10.1007/s00013-019-01348-z.","mla":"Kirschmer, Markus. “Determinant Groups of Hermitian Lattices over Local Fields.” Archiv Der Mathematik, vol. 113, no. 4, Springer Science and Business Media LLC, 2019, pp. 337–47, doi:10.1007/s00013-019-01348-z.","bibtex":"@article{Kirschmer_2019, title={Determinant groups of Hermitian lattices over local fields}, volume={113}, DOI={10.1007/s00013-019-01348-z}, 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.","ieee":"M. Kirschmer, “Determinant groups of Hermitian lattices over local fields,” Archiv der Mathematik, vol. 113, no. 4, pp. 337–347, 2019, doi: 10.1007/s00013-019-01348-z."},"page":"337-347","issue":"4","_id":"34915","intvolume":" 113","status":"public","date_created":"2022-12-23T11:03:41Z","volume":113,"publisher":"Springer Science and Business Media LLC","author":[{"full_name":"Kirschmer, Markus","first_name":"Markus","id":"82258","last_name":"Kirschmer"}],"publication":"Archiv der Mathematik","keyword":["General Mathematics"],"user_id":"93826","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"}],"language":[{"iso":"eng"}],"doi":"10.1007/s00013-019-01348-z","date_updated":"2023-04-04T09:05:04Z","publication_status":"published","publication_identifier":{"issn":["0003-889X","1420-8938"]},"department":[{"_id":"102"}],"title":"Determinant groups of Hermitian lattices over local fields"},{"department":[{"_id":"102"}],"publication_identifier":{"issn":["1793-0421","1793-7310"]},"publication_status":"published","title":"Quaternary quadratic lattices over number fields","language":[{"iso":"eng"}],"date_updated":"2023-12-06T10:05:59Z","doi":"10.1142/s1793042119500131","author":[{"id":"82258","last_name":"Kirschmer","full_name":"Kirschmer, Markus","first_name":"Markus"},{"full_name":"Nebe, Gabriele","first_name":"Gabriele","last_name":"Nebe"}],"publisher":"World Scientific Pub Co Pte Lt","keyword":["Algebra and Number Theory"],"publication":"International Journal of Number Theory","volume":15,"status":"public","date_created":"2022-12-23T11:05:09Z","abstract":[{"lang":"eng","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)."}],"user_id":"82258","year":"2019","type":"journal_article","citation":{"mla":"Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over Number Fields.” International Journal of Number Theory, vol. 15, no. 02, World Scientific Pub Co Pte Lt, 2019, pp. 309–25, doi:10.1142/s1793042119500131.","bibtex":"@article{Kirschmer_Nebe_2019, title={Quaternary quadratic lattices over number fields}, volume={15}, DOI={10.1142/s1793042119500131}, 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} }","chicago":"Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over Number Fields.” International Journal of Number Theory 15, no. 02 (2019): 309–25. https://doi.org/10.1142/s1793042119500131.","ama":"Kirschmer M, Nebe G. Quaternary quadratic lattices over number fields. International Journal of Number Theory. 2019;15(02):309-325. doi:10.1142/s1793042119500131","apa":"Kirschmer, M., & Nebe, G. (2019). Quaternary quadratic lattices over number fields. International Journal of Number Theory, 15(02), 309–325. https://doi.org/10.1142/s1793042119500131","ieee":"M. Kirschmer and G. Nebe, “Quaternary quadratic lattices over number fields,” International Journal of Number Theory, vol. 15, no. 02, pp. 309–325, 2019, doi: 10.1142/s1793042119500131.","short":"M. Kirschmer, G. Nebe, International Journal of Number Theory 15 (2019) 309–325."},"page":"309-325","intvolume":" 15","_id":"34917","issue":"02"},{"intvolume":" 197","_id":"34916","type":"journal_article","citation":{"chicago":"Kirschmer, Markus. “Automorphisms of Even Unimodular Lattices over Number Fields.” Journal of Number Theory 197 (2019): 121–34. https://doi.org/10.1016/j.jnt.2018.08.004.","ama":"Kirschmer M. Automorphisms of even unimodular lattices over number fields. Journal of Number Theory. 2019;197:121-134. doi:10.1016/j.jnt.2018.08.004","apa":"Kirschmer, M. (2019). Automorphisms of even unimodular lattices over number fields. Journal of Number Theory, 197, 121–134. https://doi.org/10.1016/j.jnt.2018.08.004","bibtex":"@article{Kirschmer_2019, title={Automorphisms of even unimodular lattices over number fields}, volume={197}, DOI={10.1016/j.jnt.2018.08.004}, 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.” Journal of Number Theory, vol. 197, Elsevier BV, 2019, pp. 121–34, doi:10.1016/j.jnt.2018.08.004.","short":"M. Kirschmer, Journal of Number Theory 197 (2019) 121–134.","ieee":"M. Kirschmer, “Automorphisms of even unimodular lattices over number fields,” Journal of Number Theory, vol. 197, pp. 121–134, 2019, doi: 10.1016/j.jnt.2018.08.004."},"year":"2019","page":"121-134","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."}],"user_id":"82258","author":[{"full_name":"Kirschmer, Markus","first_name":"Markus","id":"82258","last_name":"Kirschmer"}],"publisher":"Elsevier BV","publication":"Journal of Number Theory","keyword":["Algebra and Number Theory"],"status":"public","date_created":"2022-12-23T11:04:34Z","volume":197,"date_updated":"2023-12-06T10:07:17Z","doi":"10.1016/j.jnt.2018.08.004","language":[{"iso":"eng"}],"title":"Automorphisms of even unimodular lattices over number fields","department":[{"_id":"102"}],"publication_identifier":{"issn":["0022-314X"]},"publication_status":"published"},{"doi":"10.1007/978-3-319-70566-8_22","_id":"42788","date_updated":"2023-04-04T09:08:19Z","language":[{"iso":"eng"}],"type":"book_chapter","year":"2018","citation":{"short":"M. Kirschmer, G. Nebe, in: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, Springer International Publishing, Cham, 2018.","ieee":"M. Kirschmer and G. Nebe, “One Class Genera of Lattice Chains Over Number Fields,” in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, Cham: Springer International Publishing, 2018.","ama":"Kirschmer M, Nebe G. One Class Genera of Lattice Chains Over Number Fields. In: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. Springer International Publishing; 2018. doi:10.1007/978-3-319-70566-8_22","apa":"Kirschmer, M., & Nebe, G. (2018). One Class Genera of Lattice Chains Over Number Fields. In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. Springer International Publishing. https://doi.org/10.1007/978-3-319-70566-8_22","chicago":"Kirschmer, Markus, and Gabriele Nebe. “One Class Genera of Lattice Chains Over Number Fields.” In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-70566-8_22.","mla":"Kirschmer, Markus, and Gabriele Nebe. “One Class Genera of Lattice Chains Over Number Fields.” Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, Springer International Publishing, 2018, doi:10.1007/978-3-319-70566-8_22.","bibtex":"@inbook{Kirschmer_Nebe_2018, place={Cham}, title={One Class Genera of Lattice Chains Over Number Fields}, DOI={10.1007/978-3-319-70566-8_22}, booktitle={Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory}, publisher={Springer International Publishing}, author={Kirschmer, Markus and Nebe, Gabriele}, year={2018} }"},"user_id":"93826","title":"One Class Genera of Lattice Chains Over Number Fields","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."}],"place":"Cham","extern":"1","date_created":"2023-03-07T08:23:48Z","status":"public","publication_status":"published","publication_identifier":{"isbn":["9783319705651","9783319705668"]},"department":[{"_id":"102"}],"publication":"Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory","publisher":"Springer International Publishing","author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","last_name":"Kirschmer","id":"82258"},{"first_name":"Gabriele","full_name":"Nebe, Gabriele","last_name":"Nebe"}]},{"language":[{"iso":"eng"}],"date_updated":"2023-04-04T09:07:32Z","doi":"10.5802/jtnb.1052","department":[{"_id":"102"}],"publication_identifier":{"issn":["1246-7405","2118-8572"]},"publication_status":"published","title":"One-class genera of exceptional groups over number fields","page":"847-857","year":"2018","citation":{"bibtex":"@article{Kirschmer_2018, title={One-class genera of exceptional groups over number fields}, volume={30}, DOI={10.5802/jtnb.1052}, 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.” Journal de Théorie Des Nombres de Bordeaux, vol. 30, no. 3, Cellule MathDoc/CEDRAM, 2018, pp. 847–57, doi:10.5802/jtnb.1052.","apa":"Kirschmer, M. (2018). One-class genera of exceptional groups over number fields. Journal de Théorie Des Nombres de Bordeaux, 30(3), 847–857. https://doi.org/10.5802/jtnb.1052","ama":"Kirschmer M. One-class genera of exceptional groups over number fields. Journal de Théorie des Nombres de Bordeaux. 2018;30(3):847-857. doi:10.5802/jtnb.1052","chicago":"Kirschmer, Markus. “One-Class Genera of Exceptional Groups over Number Fields.” Journal de Théorie Des Nombres de Bordeaux 30, no. 3 (2018): 847–57. https://doi.org/10.5802/jtnb.1052.","ieee":"M. Kirschmer, “One-class genera of exceptional groups over number fields,” Journal de Théorie des Nombres de Bordeaux, vol. 30, no. 3, pp. 847–857, 2018, doi: 10.5802/jtnb.1052.","short":"M. Kirschmer, Journal de Théorie Des Nombres de Bordeaux 30 (2018) 847–857."},"type":"journal_article","_id":"42790","intvolume":" 30","issue":"3","publication":"Journal de Théorie des Nombres de Bordeaux","keyword":["Algebra and Number Theory"],"publisher":"Cellule MathDoc/CEDRAM","author":[{"full_name":"Kirschmer, Markus","first_name":"Markus","id":"82258","last_name":"Kirschmer"}],"volume":30,"date_created":"2023-03-07T08:27:36Z","status":"public","extern":"1","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"}],"user_id":"93826"},{"intvolume":" 480","_id":"42791","page":"519-548","year":"2017","type":"journal_article","citation":{"short":"M. Kirschmer, M.G. Rüther, Journal of Algebra 480 (2017) 519–548.","ieee":"M. Kirschmer and M. G. Rüther, “The constructive membership problem for discrete two-generator subgroups of SL(2,R),” Journal of Algebra, vol. 480, pp. 519–548, 2017, doi: 10.1016/j.jalgebra.2017.02.029.","chicago":"Kirschmer, Markus, and Marion G. Rüther. “The Constructive Membership Problem for Discrete Two-Generator Subgroups of SL(2,R).” Journal of Algebra 480 (2017): 519–48. https://doi.org/10.1016/j.jalgebra.2017.02.029.","ama":"Kirschmer M, Rüther MG. The constructive membership problem for discrete two-generator subgroups of SL(2,R). Journal of Algebra. 2017;480:519-548. doi:10.1016/j.jalgebra.2017.02.029","apa":"Kirschmer, M., & Rüther, M. G. (2017). The constructive membership problem for discrete two-generator subgroups of SL(2,R). Journal of Algebra, 480, 519–548. https://doi.org/10.1016/j.jalgebra.2017.02.029","bibtex":"@article{Kirschmer_Rüther_2017, title={The constructive membership problem for discrete two-generator subgroups of SL(2,R)}, volume={480}, DOI={10.1016/j.jalgebra.2017.02.029}, journal={Journal of Algebra}, publisher={Elsevier BV}, author={Kirschmer, Markus and Rüther, Marion G.}, year={2017}, pages={519–548} }","mla":"Kirschmer, Markus, and Marion G. Rüther. “The Constructive Membership Problem for Discrete Two-Generator Subgroups of SL(2,R).” Journal of Algebra, vol. 480, Elsevier BV, 2017, pp. 519–48, doi:10.1016/j.jalgebra.2017.02.029."},"user_id":"93826","extern":"1","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."}],"volume":480,"date_created":"2023-03-07T08:28:11Z","status":"public","keyword":["Algebra and Number Theory"],"publication":"Journal of Algebra","publisher":"Elsevier BV","author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","last_name":"Kirschmer","id":"82258"},{"last_name":"Rüther","full_name":"Rüther, Marion G.","first_name":"Marion G."}],"doi":"10.1016/j.jalgebra.2017.02.029","date_updated":"2023-04-04T09:10:14Z","language":[{"iso":"eng"}],"title":"The constructive membership problem for discrete two-generator subgroups of SL(2,R)","publication_identifier":{"issn":["0021-8693"]},"publication_status":"published","department":[{"_id":"102"}]},{"title":"Ternary quadratic forms over number fields with small class number","publication_status":"published","publication_identifier":{"issn":["0022-314X"]},"department":[{"_id":"102"}],"doi":"10.1016/j.jnt.2014.11.001","date_updated":"2023-04-04T09:10:42Z","language":[{"iso":"eng"}],"user_id":"93826","abstract":[{"lang":"eng","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."}],"extern":"1","date_created":"2023-03-07T08:28:46Z","status":"public","volume":161,"keyword":["Algebra and Number Theory"],"publication":"Journal of Number Theory","publisher":"Elsevier BV","author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","last_name":"Kirschmer","id":"82258"},{"last_name":"Lorch","first_name":"David","full_name":"Lorch, David"}],"intvolume":" 161","_id":"42792","page":"343-361","year":"2016","citation":{"bibtex":"@article{Kirschmer_Lorch_2016, title={Ternary quadratic forms over number fields with small class number}, volume={161}, DOI={10.1016/j.jnt.2014.11.001}, 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.” Journal of Number Theory, vol. 161, Elsevier BV, 2016, pp. 343–61, doi:10.1016/j.jnt.2014.11.001.","apa":"Kirschmer, M., & Lorch, D. (2016). Ternary quadratic forms over number fields with small class number. Journal of Number Theory, 161, 343–361. https://doi.org/10.1016/j.jnt.2014.11.001","ama":"Kirschmer M, Lorch D. Ternary quadratic forms over number fields with small class number. Journal of Number Theory. 2016;161:343-361. doi:10.1016/j.jnt.2014.11.001","chicago":"Kirschmer, Markus, and David Lorch. “Ternary Quadratic Forms over Number Fields with Small Class Number.” Journal of Number Theory 161 (2016): 343–61. https://doi.org/10.1016/j.jnt.2014.11.001.","ieee":"M. Kirschmer and D. Lorch, “Ternary quadratic forms over number fields with small class number,” Journal of Number Theory, vol. 161, pp. 343–361, 2016, doi: 10.1016/j.jnt.2014.11.001.","short":"M. Kirschmer, D. Lorch, Journal of Number Theory 161 (2016) 343–361."},"type":"journal_article"},{"citation":{"apa":"Kirschmer, M. (2016). Definite quadratic and hermitian forms with small class number (Habilitation).","ama":"Kirschmer M. Definite Quadratic and Hermitian Forms with Small Class Number (Habilitation).; 2016.","chicago":"Kirschmer, Markus. Definite Quadratic and Hermitian Forms with Small Class Number (Habilitation). RWTH Aachen University, 2016.","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. Definite Quadratic and Hermitian Forms with Small Class Number (Habilitation). 2016.","short":"M. Kirschmer, Definite Quadratic and Hermitian Forms with Small Class Number (Habilitation), RWTH Aachen University, 2016.","ieee":"M. Kirschmer, Definite quadratic and hermitian forms with small class number (Habilitation). RWTH Aachen University, 2016."},"type":"misc","year":"2016","page":"166","language":[{"iso":"eng"}],"_id":"43454","date_updated":"2023-04-11T08:11:20Z","author":[{"full_name":"Kirschmer, Markus","first_name":"Markus","id":"82258","last_name":"Kirschmer"}],"department":[{"_id":"102"}],"status":"public","date_created":"2023-04-11T08:06:35Z","extern":"1","place":"RWTH Aachen University","abstract":[{"text":"Die Gitter von Klassenzahl eins oder zwei sind hier verfügbar: http://www.math.rwth-aachen.de/~Markus.Kirschmer/forms/","lang":"eng"}],"title":"Definite quadratic and hermitian forms with small class number (Habilitation)","user_id":"93826"},{"_id":"42793","intvolume":" 136","year":"2014","citation":{"ieee":"M. Kirschmer, “One-class genera of maximal integral quadratic forms,” Journal of Number Theory, vol. 136, pp. 375–393, 2014, doi: 10.1016/j.jnt.2013.10.007.","short":"M. Kirschmer, Journal of Number Theory 136 (2014) 375–393.","bibtex":"@article{Kirschmer_2014, title={One-class genera of maximal integral quadratic forms}, volume={136}, DOI={10.1016/j.jnt.2013.10.007}, 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.” Journal of Number Theory, vol. 136, Elsevier BV, 2014, pp. 375–93, doi:10.1016/j.jnt.2013.10.007.","apa":"Kirschmer, M. (2014). One-class genera of maximal integral quadratic forms. Journal of Number Theory, 136, 375–393. https://doi.org/10.1016/j.jnt.2013.10.007","ama":"Kirschmer M. One-class genera of maximal integral quadratic forms. Journal of Number Theory. 2014;136:375-393. doi:10.1016/j.jnt.2013.10.007","chicago":"Kirschmer, Markus. “One-Class Genera of Maximal Integral Quadratic Forms.” Journal of Number Theory 136 (2014): 375–93. https://doi.org/10.1016/j.jnt.2013.10.007."},"type":"journal_article","page":"375-393","extern":"1","abstract":[{"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.","lang":"eng"}],"user_id":"93826","author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","last_name":"Kirschmer","id":"82258"}],"publisher":"Elsevier BV","keyword":["Algebra and Number Theory"],"publication":"Journal of Number Theory","volume":136,"status":"public","date_created":"2023-03-07T08:29:34Z","date_updated":"2023-04-04T09:13:29Z","doi":"10.1016/j.jnt.2013.10.007","language":[{"iso":"eng"}],"title":"One-class genera of maximal integral quadratic forms","department":[{"_id":"102"}],"publication_identifier":{"issn":["0022-314X"]},"publication_status":"published"},{"department":[{"_id":"102"}],"publication_identifier":{"issn":["0017-0895","1469-509X"]},"publication_status":"published","title":"Computing with subgroups of the modular group ","language":[{"iso":"eng"}],"date_updated":"2023-04-04T07:55:16Z","doi":"10.1017/s0017089514000202","publication":"Glasgow Mathematical Journal","keyword":["General Mathematics"],"publisher":"Cambridge University Press (CUP)","author":[{"full_name":"Kirschmer, Markus","first_name":"Markus","id":"82258","last_name":"Kirschmer"},{"first_name":"CHARLES","full_name":"LEEDHAM-GREEN, CHARLES","last_name":"LEEDHAM-GREEN"}],"volume":57,"date_created":"2023-03-07T08:47:42Z","status":"public","extern":"1","abstract":[{"lang":"eng","text":"We exhibit a practical algorithm for solving the constructive membership problem for discrete free subgroups of rank 2 in PSL₂(R) or SL₂(R). This algorithm, together with methods for checking whether a two-generator subgroup of PSL₂(R) or SL₂(R) is discrete and free, have been implemented in Magma for groups defined over real algebraic number fields."}],"user_id":"93826","page":"173-180","year":"2014","citation":{"ieee":"M. Kirschmer and C. LEEDHAM-GREEN, “Computing with subgroups of the modular group ,” Glasgow Mathematical Journal, vol. 57, no. 1, pp. 173–180, 2014, doi: 10.1017/s0017089514000202.","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 .” Glasgow Mathematical Journal, vol. 57, no. 1, Cambridge University Press (CUP), 2014, pp. 173–80, doi:10.1017/s0017089514000202.","bibtex":"@article{Kirschmer_LEEDHAM-GREEN_2014, title={Computing with subgroups of the modular group }, volume={57}, DOI={10.1017/s0017089514000202}, number={1}, journal={Glasgow Mathematical Journal}, publisher={Cambridge University Press (CUP)}, author={Kirschmer, Markus and LEEDHAM-GREEN, CHARLES}, year={2014}, pages={173–180} }","chicago":"Kirschmer, Markus, and CHARLES LEEDHAM-GREEN. “Computing with Subgroups of the Modular Group .” Glasgow Mathematical Journal 57, no. 1 (2014): 173–80. https://doi.org/10.1017/s0017089514000202.","apa":"Kirschmer, M., & LEEDHAM-GREEN, C. (2014). Computing with subgroups of the modular group . Glasgow Mathematical Journal, 57(1), 173–180. https://doi.org/10.1017/s0017089514000202","ama":"Kirschmer M, LEEDHAM-GREEN C. Computing with subgroups of the modular group . Glasgow Mathematical Journal. 2014;57(1):173-180. doi:10.1017/s0017089514000202"},"type":"journal_article","intvolume":" 57","_id":"42801","issue":"1"},{"date_updated":"2023-04-04T09:31:17Z","doi":"10.1112/s1461157014000047","language":[{"iso":"eng"}],"title":"The constructive membership problem for discrete free subgroups of rank 2 of SL₂(R)","department":[{"_id":"102"}],"publication_identifier":{"issn":["1461-1570"]},"publication_status":"published","_id":"42794","intvolume":" 17","issue":"1","page":"345-359","citation":{"ama":"Eick B, Kirschmer M, Leedham-Green C. The constructive membership problem for discrete free subgroups of rank 2 of SL₂(R). LMS Journal of Computation and Mathematics. 2014;17(1):345-359. doi:10.1112/s1461157014000047","apa":"Eick, B., Kirschmer, M., & Leedham-Green, C. (2014). The constructive membership problem for discrete free subgroups of rank 2 of SL₂(R). LMS Journal of Computation and Mathematics, 17(1), 345–359. https://doi.org/10.1112/s1461157014000047","chicago":"Eick, B., Markus Kirschmer, and C. Leedham-Green. “The Constructive Membership Problem for Discrete Free Subgroups of Rank 2 of SL₂(R).” LMS Journal of Computation and Mathematics 17, no. 1 (2014): 345–59. https://doi.org/10.1112/s1461157014000047.","mla":"Eick, B., et al. “The Constructive Membership Problem for Discrete Free Subgroups of Rank 2 of SL₂(R).” LMS Journal of Computation and Mathematics, vol. 17, no. 1, Wiley, 2014, pp. 345–59, doi:10.1112/s1461157014000047.","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={10.1112/s1461157014000047}, 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.","ieee":"B. Eick, M. Kirschmer, and C. Leedham-Green, “The constructive membership problem for discrete free subgroups of rank 2 of SL₂(R),” LMS Journal of Computation and Mathematics, vol. 17, no. 1, pp. 345–359, 2014, doi: 10.1112/s1461157014000047."},"year":"2014","type":"journal_article","extern":"1","abstract":[{"lang":"eng","text":"We exhibit a practical algorithm for solving the constructive membership problem for discrete free subgroups of rank 2 in PSL₂(R) or SL₂(R). This algorithm, together with methods for checking whether a two-generator subgroup of PSL₂(R) or SL₂(R) is discrete and free, have been implemented in Magma for groups defined over real algebraic number fields."}],"user_id":"93826","publication":"LMS Journal of Computation and Mathematics","keyword":["Computational Theory and Mathematics","General Mathematics"],"author":[{"last_name":"Eick","first_name":"B.","full_name":"Eick, B."},{"first_name":"Markus","full_name":"Kirschmer, Markus","last_name":"Kirschmer","id":"82258"},{"first_name":"C.","full_name":"Leedham-Green, C.","last_name":"Leedham-Green"}],"publisher":"Wiley","volume":17,"date_created":"2023-03-07T08:30:15Z","status":"public"},{"doi":"10.1515/9783110298161.212","_id":"42805","date_updated":"2023-04-04T09:17:32Z","citation":{"short":"M. Kirschmer, M.H. Mertens, in: Integers, DE GRUYTER, 2013.","ieee":"M. Kirschmer and M. H. Mertens, “On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves,” 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 Integers. DE GRUYTER, 2013. https://doi.org/10.1515/9783110298161.212.","ama":"Kirschmer M, Mertens MH. On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves. In: Integers. DE GRUYTER; 2013. doi:10.1515/9783110298161.212","apa":"Kirschmer, M., & Mertens, M. H. (2013). On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves. In Integers. DE GRUYTER. https://doi.org/10.1515/9783110298161.212","mla":"Kirschmer, Markus, and Michael H. Mertens. “On an Analogue to the Lucas-Lehmer-Riesel Test Using Elliptic Curves.” Integers, DE GRUYTER, 2013, doi:10.1515/9783110298161.212.","bibtex":"@inbook{Kirschmer_Mertens_2013, title={On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves}, DOI={10.1515/9783110298161.212}, booktitle={Integers}, publisher={DE GRUYTER}, author={Kirschmer, Markus and Mertens, Michael H.}, year={2013} }"},"year":"2013","type":"book_chapter","language":[{"iso":"eng"}],"title":"On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves","user_id":"93826","extern":"1","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"}],"publication_status":"published","publication_identifier":{"isbn":["9783110298116"]},"status":"public","date_created":"2023-03-07T08:51:46Z","publisher":"DE GRUYTER","author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","last_name":"Kirschmer","id":"82258"},{"last_name":"Mertens","full_name":"Mertens, Michael H.","first_name":"Michael H."}],"publication":"Integers","department":[{"_id":"102"}]},{"keyword":["Computational Theory and Mathematics","General Mathematics"],"publication":"LMS Journal of Computation and Mathematics","author":[{"last_name":"Lorch","first_name":"David","full_name":"Lorch, David"},{"first_name":"Markus","full_name":"Kirschmer, Markus","last_name":"Kirschmer","id":"82258"}],"publisher":"Wiley","date_created":"2023-03-07T08:34:28Z","status":"public","volume":16,"abstract":[{"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.","lang":"eng"}],"extern":"1","user_id":"93826","page":"172-186","year":"2013","citation":{"ieee":"D. Lorch and M. Kirschmer, “Single-class genera of positive integral lattices,” LMS Journal of Computation and Mathematics, vol. 16, pp. 172–186, 2013, doi: 10.1112/s1461157013000107.","short":"D. Lorch, M. Kirschmer, LMS Journal of Computation and Mathematics 16 (2013) 172–186.","bibtex":"@article{Lorch_Kirschmer_2013, title={Single-class genera of positive integral lattices}, volume={16}, DOI={10.1112/s1461157013000107}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Lorch, David and Kirschmer, Markus}, year={2013}, pages={172–186} }","mla":"Lorch, David, and Markus Kirschmer. “Single-Class Genera of Positive Integral Lattices.” LMS Journal of Computation and Mathematics, vol. 16, Wiley, 2013, pp. 172–86, doi:10.1112/s1461157013000107.","chicago":"Lorch, David, and Markus Kirschmer. “Single-Class Genera of Positive Integral Lattices.” LMS Journal of Computation and Mathematics 16 (2013): 172–86. https://doi.org/10.1112/s1461157013000107.","apa":"Lorch, D., & Kirschmer, M. (2013). Single-class genera of positive integral lattices. LMS Journal of Computation and Mathematics, 16, 172–186. https://doi.org/10.1112/s1461157013000107","ama":"Lorch D, Kirschmer M. Single-class genera of positive integral lattices. LMS Journal of Computation and Mathematics. 2013;16:172-186. doi:10.1112/s1461157013000107"},"type":"journal_article","_id":"42796","intvolume":" 16","department":[{"_id":"102"}],"publication_identifier":{"issn":["1461-1570"]},"publication_status":"published","title":"Single-class genera of positive integral lattices","language":[{"iso":"eng"}],"date_updated":"2023-04-04T07:57:04Z","doi":"10.1112/s1461157013000107"},{"volume":81,"status":"public","date_created":"2023-03-07T08:35:56Z","author":[{"full_name":"Kirschmer, Markus","first_name":"Markus","id":"82258","last_name":"Kirschmer"}],"publisher":"American Mathematical Society (AMS)","publication":"Mathematics of Computation","keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"user_id":"93826","extern":"1","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"}],"citation":{"mla":"Kirschmer, Markus. “A Normal Form for Definite Quadratic Forms over $\\mathbb{F}_{q}[t]$.” Mathematics of Computation, vol. 81, no. 279, American Mathematical Society (AMS), 2012, pp. 1619–34, doi:10.1090/s0025-5718-2011-02570-6.","bibtex":"@article{Kirschmer_2012, title={A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$}, volume={81}, DOI={10.1090/s0025-5718-2011-02570-6}, number={279}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Kirschmer, Markus}, year={2012}, pages={1619–1634} }","chicago":"Kirschmer, Markus. “A Normal Form for Definite Quadratic Forms over $\\mathbb{F}_{q}[t]$.” Mathematics of Computation 81, no. 279 (2012): 1619–34. https://doi.org/10.1090/s0025-5718-2011-02570-6.","ama":"Kirschmer M. A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$. Mathematics of Computation. 2012;81(279):1619-1634. doi:10.1090/s0025-5718-2011-02570-6","apa":"Kirschmer, M. (2012). A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$. Mathematics of Computation, 81(279), 1619–1634. https://doi.org/10.1090/s0025-5718-2011-02570-6","ieee":"M. Kirschmer, “A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$,” Mathematics of Computation, vol. 81, no. 279, pp. 1619–1634, 2012, doi: 10.1090/s0025-5718-2011-02570-6.","short":"M. Kirschmer, Mathematics of Computation 81 (2012) 1619–1634."},"year":"2012","type":"journal_article","page":"1619-1634","issue":"279","intvolume":" 81","_id":"42797","publication_status":"published","publication_identifier":{"issn":["0025-5718","1088-6842"]},"department":[{"_id":"102"}],"title":"A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$","language":[{"iso":"eng"}],"doi":"10.1090/s0025-5718-2011-02570-6","date_updated":"2023-04-04T09:22:22Z"},{"title":"Finite Symplectic Matrix Groups","publication_identifier":{"issn":["1058-6458","1944-950X"]},"publication_status":"published","department":[{"_id":"102"}],"doi":"10.1080/10586458.2011.564964","date_updated":"2023-04-04T09:24:42Z","language":[{"iso":"eng"}],"user_id":"93826","extern":"1","abstract":[{"lang":"eng","text":"This paper classifies the maximal finite subgroups of SP₂ₙ(Q) for 1⩽n⩽11 up to GL₂ₙ(Q) conjugacy in ."}],"volume":20,"date_created":"2023-03-07T08:36:46Z","status":"public","keyword":["General Mathematics"],"publication":"Experimental Mathematics","author":[{"last_name":"Kirschmer","id":"82258","first_name":"Markus","full_name":"Kirschmer, Markus"}],"publisher":"Informa UK Limited","issue":"2","_id":"42798","intvolume":" 20","page":"217-228","citation":{"ieee":"M. Kirschmer, “Finite Symplectic Matrix Groups,” Experimental Mathematics, vol. 20, no. 2, pp. 217–228, 2011, doi: 10.1080/10586458.2011.564964.","short":"M. Kirschmer, Experimental Mathematics 20 (2011) 217–228.","bibtex":"@article{Kirschmer_2011, title={Finite Symplectic Matrix Groups}, volume={20}, DOI={10.1080/10586458.2011.564964}, number={2}, journal={Experimental Mathematics}, publisher={Informa UK Limited}, author={Kirschmer, Markus}, year={2011}, pages={217–228} }","mla":"Kirschmer, Markus. “Finite Symplectic Matrix Groups.” Experimental Mathematics, vol. 20, no. 2, Informa UK Limited, 2011, pp. 217–28, doi:10.1080/10586458.2011.564964.","ama":"Kirschmer M. Finite Symplectic Matrix Groups. Experimental Mathematics. 2011;20(2):217-228. doi:10.1080/10586458.2011.564964","apa":"Kirschmer, M. (2011). Finite Symplectic Matrix Groups. Experimental Mathematics, 20(2), 217–228. https://doi.org/10.1080/10586458.2011.564964","chicago":"Kirschmer, Markus. “Finite Symplectic Matrix Groups.” Experimental Mathematics 20, no. 2 (2011): 217–28. https://doi.org/10.1080/10586458.2011.564964."},"year":"2011","type":"journal_article"},{"user_id":"93826","abstract":[{"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.","lang":"eng"}],"extern":"1","status":"public","date_created":"2023-03-07T08:49:35Z","volume":39,"author":[{"last_name":"Kirschmer","id":"82258","first_name":"Markus","full_name":"Kirschmer, Markus"},{"last_name":"Voight","first_name":"John","full_name":"Voight, John"}],"publisher":"Society for Industrial & Applied Mathematics (SIAM)","publication":"SIAM Journal on Computing","keyword":["General Mathematics","General Computer Science"],"issue":"5","_id":"42803","intvolume":" 39","year":"2010","type":"journal_article","citation":{"ieee":"M. Kirschmer and J. Voight, “Algorithmic Enumeration of Ideal Classes for Quaternion Orders,” SIAM Journal on Computing, vol. 39, no. 5, pp. 1714–1747, 2010, doi: 10.1137/080734467.","short":"M. Kirschmer, J. Voight, SIAM Journal on Computing 39 (2010) 1714–1747.","mla":"Kirschmer, Markus, and John Voight. “Algorithmic Enumeration of Ideal Classes for Quaternion Orders.” SIAM Journal on Computing, vol. 39, no. 5, Society for Industrial & Applied Mathematics (SIAM), 2010, pp. 1714–47, doi:10.1137/080734467.","bibtex":"@article{Kirschmer_Voight_2010, title={Algorithmic Enumeration of Ideal Classes for Quaternion Orders}, volume={39}, DOI={10.1137/080734467}, number={5}, journal={SIAM Journal on Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kirschmer, Markus and Voight, John}, year={2010}, pages={1714–1747} }","chicago":"Kirschmer, Markus, and John Voight. “Algorithmic Enumeration of Ideal Classes for Quaternion Orders.” SIAM Journal on Computing 39, no. 5 (2010): 1714–47. https://doi.org/10.1137/080734467.","apa":"Kirschmer, M., & Voight, J. (2010). Algorithmic Enumeration of Ideal Classes for Quaternion Orders. SIAM Journal on Computing, 39(5), 1714–1747. https://doi.org/10.1137/080734467","ama":"Kirschmer M, Voight J. Algorithmic Enumeration of Ideal Classes for Quaternion Orders. SIAM Journal on Computing. 2010;39(5):1714-1747. doi:10.1137/080734467"},"page":"1714-1747","title":"Algorithmic Enumeration of Ideal Classes for Quaternion Orders","publication_identifier":{"issn":["0097-5397","1095-7111"]},"publication_status":"published","department":[{"_id":"102"}],"doi":"10.1137/080734467","date_updated":"2023-04-04T09:25:08Z","language":[{"iso":"eng"}]},{"extern":"1","abstract":[{"lang":"eng","text":"Die invarianten Formen aus dem Anhang sind hier verfügbar:http://www.math.rwth-aachen.de/homes/Markus.Kirschmer/symplectic/"}],"place":"RWTH Aachen University","title":"Finite symplectic matrix groups (Dissertation)","user_id":"93826","department":[{"_id":"102"}],"author":[{"full_name":"Kirschmer, Markus","first_name":"Markus","id":"82258","last_name":"Kirschmer"}],"date_created":"2023-04-11T08:03:29Z","status":"public","date_updated":"2023-04-11T08:14:10Z","_id":"43453","page":"149","type":"dissertation","year":"2009","citation":{"short":"M. Kirschmer, Finite Symplectic Matrix Groups (Dissertation), RWTH Aachen University, 2009.","ieee":"M. Kirschmer, Finite symplectic matrix groups (Dissertation). RWTH Aachen University, 2009.","ama":"Kirschmer M. Finite Symplectic Matrix Groups (Dissertation).; 2009.","apa":"Kirschmer, M. (2009). Finite symplectic matrix groups (Dissertation).","chicago":"Kirschmer, Markus. Finite Symplectic Matrix Groups (Dissertation). RWTH Aachen University, 2009.","mla":"Kirschmer, Markus. Finite Symplectic Matrix Groups (Dissertation). 2009.","bibtex":"@book{Kirschmer_2009, place={RWTH Aachen University}, title={Finite symplectic matrix groups (Dissertation)}, author={Kirschmer, Markus}, year={2009} }"},"language":[{"iso":"eng"}]}]