[{"status":"public","type":"journal_article","publication":"Int. Math. Res. Not. IMRN","language":[{"iso":"eng"}],"user_id":"106108","department":[{"_id":"102"}],"_id":"55276","citation":{"ama":"Minelli P, Sourmelidis A, Technau M. On restricted averages of Dedekind sums. <i>Int Math Res Not IMRN</i>. 2024;2024(10):8485–8502. doi:<a href=\"https://doi.org/10.1093/imrn/rnad283\">10.1093/imrn/rnad283</a>","ieee":"P. Minelli, A. Sourmelidis, and M. Technau, “On restricted averages of Dedekind sums,” <i>Int. Math. Res. Not. IMRN</i>, vol. 2024, no. 10, pp. 8485–8502, 2024, doi: <a href=\"https://doi.org/10.1093/imrn/rnad283\">10.1093/imrn/rnad283</a>.","chicago":"Minelli, P., A. Sourmelidis, and Marc Technau. “On Restricted Averages of Dedekind Sums.” <i>Int. Math. Res. Not. IMRN</i> 2024, no. 10 (2024): 8485–8502. <a href=\"https://doi.org/10.1093/imrn/rnad283\">https://doi.org/10.1093/imrn/rnad283</a>.","apa":"Minelli, P., Sourmelidis, A., &#38; Technau, M. (2024). On restricted averages of Dedekind sums. <i>Int. Math. Res. Not. IMRN</i>, <i>2024</i>(10), 8485–8502. <a href=\"https://doi.org/10.1093/imrn/rnad283\">https://doi.org/10.1093/imrn/rnad283</a>","short":"P. Minelli, A. Sourmelidis, M. Technau, Int. Math. Res. Not. IMRN 2024 (2024) 8485–8502.","mla":"Minelli, P., et al. “On Restricted Averages of Dedekind Sums.” <i>Int. Math. Res. Not. IMRN</i>, vol. 2024, no. 10, 2024, pp. 8485–8502, doi:<a href=\"https://doi.org/10.1093/imrn/rnad283\">10.1093/imrn/rnad283</a>.","bibtex":"@article{Minelli_Sourmelidis_Technau_2024, title={On restricted averages of Dedekind sums}, volume={2024}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnad283\">10.1093/imrn/rnad283</a>}, number={10}, journal={Int. Math. Res. Not. IMRN}, author={Minelli, P. and Sourmelidis, A. and Technau, Marc}, year={2024}, pages={8485–8502} }"},"page":"8485–8502","intvolume":"      2024","year":"2024","issue":"10","doi":"10.1093/imrn/rnad283","title":"On restricted averages of Dedekind sums","author":[{"full_name":"Minelli, P.","last_name":"Minelli","first_name":"P."},{"last_name":"Sourmelidis","full_name":"Sourmelidis, A.","first_name":"A."},{"orcid":"0000-0001-9650-2459","last_name":"Technau","full_name":"Technau, Marc","id":"106108","first_name":"Marc"}],"date_created":"2024-07-16T11:09:00Z","volume":2024,"date_updated":"2024-07-24T07:23:20Z"},{"status":"public","publication":"Proc. Amer. Math. Soc.","type":"journal_article","extern":"1","language":[{"iso":"eng"}],"department":[{"_id":"102"}],"user_id":"106108","_id":"55278","page":"63–69","intvolume":"       152","citation":{"apa":"Technau, M. (2024). Remark on the Farey fraction spin chain. <i>Proc. Amer. Math. Soc.</i>, <i>152</i>(1), 63–69. <a href=\"https://doi.org/10.1090/proc/16520\">https://doi.org/10.1090/proc/16520</a>","mla":"Technau, Marc. “Remark on the Farey Fraction Spin Chain.” <i>Proc. Amer. Math. Soc.</i>, vol. 152, no. 1, 2024, pp. 63–69, doi:<a href=\"https://doi.org/10.1090/proc/16520\">10.1090/proc/16520</a>.","short":"M. Technau, Proc. Amer. Math. Soc. 152 (2024) 63–69.","bibtex":"@article{Technau_2024, title={Remark on the Farey fraction spin chain}, volume={152}, DOI={<a href=\"https://doi.org/10.1090/proc/16520\">10.1090/proc/16520</a>}, number={1}, journal={Proc. Amer. Math. Soc.}, author={Technau, Marc}, year={2024}, pages={63–69} }","ama":"Technau M. Remark on the Farey fraction spin chain. <i>Proc Amer Math Soc</i>. 2024;152(1):63–69. doi:<a href=\"https://doi.org/10.1090/proc/16520\">10.1090/proc/16520</a>","ieee":"M. Technau, “Remark on the Farey fraction spin chain,” <i>Proc. Amer. Math. Soc.</i>, vol. 152, no. 1, pp. 63–69, 2024, doi: <a href=\"https://doi.org/10.1090/proc/16520\">10.1090/proc/16520</a>.","chicago":"Technau, Marc. “Remark on the Farey Fraction Spin Chain.” <i>Proc. Amer. Math. Soc.</i> 152, no. 1 (2024): 63–69. <a href=\"https://doi.org/10.1090/proc/16520\">https://doi.org/10.1090/proc/16520</a>."},"year":"2024","issue":"1","doi":"10.1090/proc/16520","title":"Remark on the Farey fraction spin chain","volume":152,"author":[{"first_name":"Marc","last_name":"Technau","orcid":"0000-0001-9650-2459","id":"106108","full_name":"Technau, Marc"}],"date_created":"2024-07-16T11:09:01Z","date_updated":"2024-07-24T07:26:12Z"},{"publication_identifier":{"issn":["2730-9657"]},"publication_status":"published","year":"2023","citation":{"apa":"Klüners, J., &#38; Wang, J. (2023). Idélic Approach in Enumerating Heisenberg Extensions. <i>La Matematica</i>. <a href=\"https://doi.org/10.1007/s44007-023-00067-w\">https://doi.org/10.1007/s44007-023-00067-w</a>","short":"J. Klüners, J. Wang, La Matematica (2023).","bibtex":"@article{Klüners_Wang_2023, title={Idélic Approach in Enumerating Heisenberg Extensions}, DOI={<a href=\"https://doi.org/10.1007/s44007-023-00067-w\">10.1007/s44007-023-00067-w</a>}, journal={La Matematica}, publisher={Springer Science and Business Media LLC}, author={Klüners, Jürgen and Wang, Jiuya}, year={2023} }","mla":"Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg Extensions.” <i>La Matematica</i>, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s44007-023-00067-w\">10.1007/s44007-023-00067-w</a>.","ieee":"J. Klüners and J. Wang, “Idélic Approach in Enumerating Heisenberg Extensions,” <i>La Matematica</i>, 2023, doi: <a href=\"https://doi.org/10.1007/s44007-023-00067-w\">10.1007/s44007-023-00067-w</a>.","chicago":"Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg Extensions.” <i>La Matematica</i>, 2023. <a href=\"https://doi.org/10.1007/s44007-023-00067-w\">https://doi.org/10.1007/s44007-023-00067-w</a>.","ama":"Klüners J, Wang J. Idélic Approach in Enumerating Heisenberg Extensions. <i>La Matematica</i>. 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Number Theory","doi":"10.1142/S1793042123501208","title":"Galois groups of (ⁿ₀)+(ⁿ₁)X+…+(ⁿ₆)X⁶","author":[{"last_name":"Klahn","full_name":"Klahn, B.","first_name":"B."},{"first_name":"Marc","orcid":"0000-0001-9650-2459","last_name":"Technau","full_name":"Technau, Marc","id":"106108"}],"date_created":"2024-07-16T11:09:01Z","volume":19,"date_updated":"2024-07-24T07:23:33Z","citation":{"apa":"Klahn, B., &#38; Technau, M. (2023). Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>. <i>Int. J. Number Theory</i>, <i>19</i>(10), 2443–2450. <a href=\"https://doi.org/10.1142/S1793042123501208\">https://doi.org/10.1142/S1793042123501208</a>","bibtex":"@article{Klahn_Technau_2023, title={Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>}, volume={19}, DOI={<a href=\"https://doi.org/10.1142/S1793042123501208\">10.1142/S1793042123501208</a>}, number={10}, journal={Int. J. Number Theory}, author={Klahn, B. and Technau, Marc}, year={2023}, pages={2443–2450} }","short":"B. Klahn, M. Technau, Int. J. Number Theory 19 (2023) 2443–2450.","mla":"Klahn, B., and Marc Technau. “Galois Groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>.” <i>Int. J. Number Theory</i>, vol. 19, no. 10, 2023, pp. 2443–2450, doi:<a href=\"https://doi.org/10.1142/S1793042123501208\">10.1142/S1793042123501208</a>.","ieee":"B. Klahn and M. Technau, “Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>,” <i>Int. J. Number Theory</i>, vol. 19, no. 10, pp. 2443–2450, 2023, doi: <a href=\"https://doi.org/10.1142/S1793042123501208\">10.1142/S1793042123501208</a>.","chicago":"Klahn, B., and Marc Technau. “Galois Groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>.” <i>Int. J. Number Theory</i> 19, no. 10 (2023): 2443–2450. <a href=\"https://doi.org/10.1142/S1793042123501208\">https://doi.org/10.1142/S1793042123501208</a>.","ama":"Klahn B, Technau M. Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>. <i>Int J Number Theory</i>. 2023;19(10):2443–2450. doi:<a href=\"https://doi.org/10.1142/S1793042123501208\">10.1142/S1793042123501208</a>"},"intvolume":"        19","page":"2443–2450","year":"2023","issue":"10"},{"publication":"Math. Ann.","type":"journal_article","status":"public","_id":"55279","department":[{"_id":"102"}],"user_id":"106108","language":[{"iso":"eng"}],"extern":"1","year":"2023","page":"291–320","intvolume":"       387","citation":{"mla":"Minelli, P., et al. “Bias in the Number of Steps in the Euclidean Algorithm and a Conjecture of Ito on Dedekind Sums.” <i>Math. Ann.</i>, vol. 387, 2023, pp. 291–320, doi:<a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>.","short":"P. Minelli, A. Sourmelidis, M. Technau, Math. Ann. 387 (2023) 291–320.","bibtex":"@article{Minelli_Sourmelidis_Technau_2023, title={Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums}, volume={387}, DOI={<a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>}, journal={Math. Ann.}, author={Minelli, P. and Sourmelidis, A. and Technau, Marc}, year={2023}, pages={291–320} }","apa":"Minelli, P., Sourmelidis, A., &#38; Technau, M. (2023). Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums. <i>Math. Ann.</i>, <i>387</i>, 291–320. <a href=\"https://doi.org/10.1007/s00208-022-02452-2\">https://doi.org/10.1007/s00208-022-02452-2</a>","ieee":"P. Minelli, A. Sourmelidis, and M. Technau, “Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums,” <i>Math. Ann.</i>, vol. 387, pp. 291–320, 2023, doi: <a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>.","chicago":"Minelli, P., A. Sourmelidis, and Marc Technau. “Bias in the Number of Steps in the Euclidean Algorithm and a Conjecture of Ito on Dedekind Sums.” <i>Math. Ann.</i> 387 (2023): 291–320. <a href=\"https://doi.org/10.1007/s00208-022-02452-2\">https://doi.org/10.1007/s00208-022-02452-2</a>.","ama":"Minelli P, Sourmelidis A, Technau M. Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums. <i>Math Ann</i>. 2023;387:291–320. doi:<a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>"},"date_updated":"2024-07-24T07:26:05Z","volume":387,"author":[{"first_name":"P.","last_name":"Minelli","full_name":"Minelli, P."},{"first_name":"A.","last_name":"Sourmelidis","full_name":"Sourmelidis, A."},{"last_name":"Technau","orcid":"0000-0001-9650-2459","full_name":"Technau, Marc","id":"106108","first_name":"Marc"}],"date_created":"2024-07-16T11:09:01Z","title":"Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums","doi":"10.1007/s00208-022-02452-2"},{"title":"On polynomials with roots modulo almost all primes","doi":"10.4064/aa220407-9-7","date_updated":"2024-07-24T07:26:22Z","volume":"205:3","date_created":"2024-07-16T11:09:01Z","author":[{"first_name":"Ch.","full_name":"Elsholtz, Ch.","last_name":"Elsholtz"},{"full_name":"Klahn, B.","last_name":"Klahn","first_name":"B."},{"last_name":"Technau","orcid":"0000-0001-9650-2459","id":"106108","full_name":"Technau, Marc","first_name":"Marc"}],"year":"2022","page":"251–263","citation":{"bibtex":"@article{Elsholtz_Klahn_Technau_2022, title={On polynomials with roots modulo almost all primes}, volume={205:3}, DOI={<a href=\"https://doi.org/10.4064/aa220407-9-7\">10.4064/aa220407-9-7</a>}, number={3}, journal={Acta Arith.}, author={Elsholtz, Ch. and Klahn, B. and Technau, Marc}, year={2022}, pages={251–263} }","short":"Ch. Elsholtz, B. Klahn, M. Technau, Acta Arith. 205:3 (2022) 251–263.","mla":"Elsholtz, Ch., et al. “On Polynomials with Roots modulo Almost All Primes.” <i>Acta Arith.</i>, vol. 205:3, no. 3, 2022, pp. 251–263, doi:<a href=\"https://doi.org/10.4064/aa220407-9-7\">10.4064/aa220407-9-7</a>.","apa":"Elsholtz, Ch., Klahn, B., &#38; Technau, M. (2022). On polynomials with roots modulo almost all primes. <i>Acta Arith.</i>, <i>205:3</i>(3), 251–263. <a href=\"https://doi.org/10.4064/aa220407-9-7\">https://doi.org/10.4064/aa220407-9-7</a>","chicago":"Elsholtz, Ch., B. Klahn, and Marc Technau. “On Polynomials with Roots modulo Almost All Primes.” <i>Acta Arith.</i> 205:3, no. 3 (2022): 251–263. <a href=\"https://doi.org/10.4064/aa220407-9-7\">https://doi.org/10.4064/aa220407-9-7</a>.","ieee":"Ch. Elsholtz, B. Klahn, and M. Technau, “On polynomials with roots modulo almost all primes,” <i>Acta Arith.</i>, vol. 205:3, no. 3, pp. 251–263, 2022, doi: <a href=\"https://doi.org/10.4064/aa220407-9-7\">10.4064/aa220407-9-7</a>.","ama":"Elsholtz Ch, Klahn B, Technau M. On polynomials with roots modulo almost all primes. <i>Acta Arith</i>. 2022;205:3(3):251–263. doi:<a href=\"https://doi.org/10.4064/aa220407-9-7\">10.4064/aa220407-9-7</a>"},"issue":"3","extern":"1","language":[{"iso":"eng"}],"_id":"55280","department":[{"_id":"102"}],"user_id":"106108","status":"public","publication":"Acta Arith.","type":"journal_article"},{"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","General Mathematics"],"external_id":{"arxiv":["2003.12161 "]},"abstract":[{"text":"We describe the relations among the ℓ-torsion conjecture, a conjecture of Malle giving an upper bound for the number of extensions, and the discriminant multiplicity conjecture. We prove that the latter two conjectures are equivalent in some sense. Altogether, the three conjectures are equivalent for the class of solvable groups. We then prove the ℓ-torsion conjecture for ℓ-groups and the other two conjectures for nilpotent groups.","lang":"eng"}],"publication":"Proceedings of the American Mathematical Society","title":"ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group","date_created":"2022-12-22T10:47:01Z","publisher":"American Mathematical Society (AMS)","year":"2022","issue":"7","department":[{"_id":"102"}],"user_id":"93826","_id":"34839","status":"public","type":"journal_article","doi":"10.1090/proc/15882","volume":150,"author":[{"last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202","first_name":"Jürgen"},{"first_name":"Jiuya","last_name":"Wang","full_name":"Wang, Jiuya"}],"date_updated":"2023-03-06T08:47:42Z","page":"2793-2805","intvolume":"       150","citation":{"ama":"Klüners J, Wang J. ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group. <i>Proceedings of the American Mathematical Society</i>. 2022;150(7):2793-2805. doi:<a href=\"https://doi.org/10.1090/proc/15882\">10.1090/proc/15882</a>","ieee":"J. Klüners and J. Wang, “ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group,” <i>Proceedings of the American Mathematical Society</i>, vol. 150, no. 7, pp. 2793–2805, 2022, doi: <a href=\"https://doi.org/10.1090/proc/15882\">10.1090/proc/15882</a>.","chicago":"Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group of Number Fields with an ℓ-Group as Galois Group.” <i>Proceedings of the American Mathematical Society</i> 150, no. 7 (2022): 2793–2805. <a href=\"https://doi.org/10.1090/proc/15882\">https://doi.org/10.1090/proc/15882</a>.","apa":"Klüners, J., &#38; Wang, J. (2022). ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group. <i>Proceedings of the American Mathematical Society</i>, <i>150</i>(7), 2793–2805. <a href=\"https://doi.org/10.1090/proc/15882\">https://doi.org/10.1090/proc/15882</a>","short":"J. Klüners, J. Wang, Proceedings of the American Mathematical Society 150 (2022) 2793–2805.","bibtex":"@article{Klüners_Wang_2022, title={ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group}, volume={150}, DOI={<a href=\"https://doi.org/10.1090/proc/15882\">10.1090/proc/15882</a>}, number={7}, journal={Proceedings of the American Mathematical Society}, publisher={American Mathematical Society (AMS)}, author={Klüners, Jürgen and Wang, Jiuya}, year={2022}, pages={2793–2805} }","mla":"Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group of Number Fields with an ℓ-Group as Galois Group.” <i>Proceedings of the American Mathematical Society</i>, vol. 150, no. 7, American Mathematical Society (AMS), 2022, pp. 2793–805, doi:<a href=\"https://doi.org/10.1090/proc/15882\">10.1090/proc/15882</a>."},"publication_identifier":{"issn":["0002-9939","1088-6826"]},"publication_status":"published"},{"author":[{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"}],"volume":204,"date_updated":"2023-03-06T08:48:33Z","doi":"10.4064/aa211207-16-5","publication_status":"published","publication_identifier":{"issn":["0065-1036","1730-6264"]},"citation":{"ama":"Klüners J. The asymptotics of nilpotent Galois groups. <i>Acta Arithmetica</i>. 2022;204(2):165-184. doi:<a href=\"https://doi.org/10.4064/aa211207-16-5\">10.4064/aa211207-16-5</a>","chicago":"Klüners, Jürgen. “The Asymptotics of Nilpotent Galois Groups.” <i>Acta Arithmetica</i> 204, no. 2 (2022): 165–84. <a href=\"https://doi.org/10.4064/aa211207-16-5\">https://doi.org/10.4064/aa211207-16-5</a>.","ieee":"J. Klüners, “The asymptotics of nilpotent Galois groups,” <i>Acta Arithmetica</i>, vol. 204, no. 2, pp. 165–184, 2022, doi: <a href=\"https://doi.org/10.4064/aa211207-16-5\">10.4064/aa211207-16-5</a>.","short":"J. Klüners, Acta Arithmetica 204 (2022) 165–184.","bibtex":"@article{Klüners_2022, title={The asymptotics of nilpotent Galois groups}, volume={204}, DOI={<a href=\"https://doi.org/10.4064/aa211207-16-5\">10.4064/aa211207-16-5</a>}, number={2}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish Academy of Sciences}, author={Klüners, Jürgen}, year={2022}, pages={165–184} }","mla":"Klüners, Jürgen. “The Asymptotics of Nilpotent Galois Groups.” <i>Acta Arithmetica</i>, vol. 204, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2022, pp. 165–84, doi:<a href=\"https://doi.org/10.4064/aa211207-16-5\">10.4064/aa211207-16-5</a>.","apa":"Klüners, J. (2022). The asymptotics of nilpotent Galois groups. <i>Acta Arithmetica</i>, <i>204</i>(2), 165–184. <a href=\"https://doi.org/10.4064/aa211207-16-5\">https://doi.org/10.4064/aa211207-16-5</a>"},"page":"165-184","intvolume":"       204","user_id":"93826","department":[{"_id":"102"}],"_id":"34835","type":"journal_article","status":"public","date_created":"2022-12-22T10:08:23Z","publisher":"Institute of Mathematics, Polish Academy of Sciences","title":"The asymptotics of nilpotent Galois groups","issue":"2","year":"2022","external_id":{"arxiv":["2011.04325 "]},"language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"publication":"Acta Arithmetica","abstract":[{"lang":"eng","text":"We prove an upper bound for the asymptotics of counting functions of number fields with nilpotent Galois groups. "}]},{"language":[{"iso":"eng"}],"keyword":["General Mathematics"],"user_id":"93826","department":[{"_id":"102"}],"_id":"45854","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","doi":"10.1080/10586458.2019.1618756","title":"Binary Hermitian Lattices over Number Fields","date_created":"2023-07-04T08:28:04Z","author":[{"full_name":"Kirschmer, Markus","id":"82258","last_name":"Kirschmer","first_name":"Markus"},{"full_name":"Nebe, Gabriele","last_name":"Nebe","first_name":"Gabriele"}],"volume":31,"date_updated":"2023-07-04T08:29:22Z","publisher":"Informa UK Limited","citation":{"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>.","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} }","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>","ama":"Kirschmer M, Nebe G. 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Zafeiropoulos. “Metric Results on Summatory Arithmetic Functions on Beatty Sets.” <i>Acta Arith.</i>, vol. 197, no. 1, 2021, pp. 93–104, doi:<a href=\"https://doi.org/10.4064/aa200128-10-6\">10.4064/aa200128-10-6</a>.","bibtex":"@article{Technau_Zafeiropoulos_2021, title={Metric results on summatory arithmetic functions on Beatty sets}, volume={197}, DOI={<a href=\"https://doi.org/10.4064/aa200128-10-6\">10.4064/aa200128-10-6</a>}, number={1}, journal={Acta Arith.}, author={Technau, Marc and Zafeiropoulos, A.}, year={2021}, pages={93–104} }","apa":"Technau, M., &#38; Zafeiropoulos, A. (2021). Metric results on summatory arithmetic functions on Beatty sets. <i>Acta Arith.</i>, <i>197</i>(1), 93–104. <a href=\"https://doi.org/10.4064/aa200128-10-6\">https://doi.org/10.4064/aa200128-10-6</a>","ama":"Technau M, Zafeiropoulos A. Metric results on summatory arithmetic functions on Beatty sets. <i>Acta Arith</i>. 2021;197(1):93–104. doi:<a href=\"https://doi.org/10.4064/aa200128-10-6\">10.4064/aa200128-10-6</a>","chicago":"Technau, Marc, and A. Zafeiropoulos. “Metric Results on Summatory Arithmetic Functions on Beatty Sets.” <i>Acta Arith.</i> 197, no. 1 (2021): 93–104. <a href=\"https://doi.org/10.4064/aa200128-10-6\">https://doi.org/10.4064/aa200128-10-6</a>.","ieee":"M. Technau and A. Zafeiropoulos, “Metric results on summatory arithmetic functions on Beatty sets,” <i>Acta Arith.</i>, vol. 197, no. 1, pp. 93–104, 2021, doi: <a href=\"https://doi.org/10.4064/aa200128-10-6\">10.4064/aa200128-10-6</a>."},"intvolume":"       197","page":"93–104","year":"2021","issue":"1","doi":"10.4064/aa200128-10-6","title":"Metric results on summatory arithmetic functions on Beatty sets","date_created":"2024-07-16T11:09:03Z","author":[{"last_name":"Technau","orcid":"0000-0001-9650-2459","id":"106108","full_name":"Technau, Marc","first_name":"Marc"},{"full_name":"Zafeiropoulos, A.","last_name":"Zafeiropoulos","first_name":"A."}],"volume":197,"date_updated":"2024-07-24T07:25:48Z","status":"public","type":"journal_article","publication":"Acta Arith.","language":[{"iso":"eng"}],"extern":"1","user_id":"106108","department":[{"_id":"102"}],"_id":"55289"},{"user_id":"93826","department":[{"_id":"102"}],"_id":"34840","type":"journal_article","status":"public","author":[{"last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202","first_name":"Jürgen"},{"first_name":"Toru","full_name":"Komatsu, Toru","last_name":"Komatsu"}],"volume":90,"date_updated":"2023-03-06T08:57:45Z","doi":"10.1090/mcom/3609","publication_status":"published","publication_identifier":{"issn":["0025-5718","1088-6842"]},"citation":{"mla":"Klüners, Jürgen, and Toru Komatsu. “Imaginary Multiquadratic Number Fields with Class Group of Exponent $3$ and $5$.” <i>Mathematics of Computation</i>, vol. 90, no. 329, American Mathematical Society (AMS), 2021, pp. 1483–97, doi:<a href=\"https://doi.org/10.1090/mcom/3609\">10.1090/mcom/3609</a>.","bibtex":"@article{Klüners_Komatsu_2021, title={Imaginary multiquadratic number fields with class group of exponent $3$ and $5$}, volume={90}, DOI={<a href=\"https://doi.org/10.1090/mcom/3609\">10.1090/mcom/3609</a>}, number={329}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Klüners, Jürgen and Komatsu, Toru}, year={2021}, pages={1483–1497} }","short":"J. 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"}],"date_created":"2022-12-22T10:48:44Z","publisher":"American Mathematical Society (AMS)","title":"Imaginary multiquadratic number fields with class group of exponent $3$ and $5$","issue":"329","year":"2021"},{"user_id":"93826","department":[{"_id":"102"}],"_id":"34912","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"type":"journal_article","publication":"Mathematics of Computation","status":"public","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. "}],"date_created":"2022-12-23T11:02:02Z","author":[{"first_name":"Markus","last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus"},{"first_name":"Fabien","full_name":"Narbonne, Fabien","last_name":"Narbonne"},{"last_name":"Ritzenthaler","full_name":"Ritzenthaler, Christophe","first_name":"Christophe"},{"full_name":"Robert, Damien","last_name":"Robert","first_name":"Damien"}],"volume":91,"date_updated":"2023-04-04T07:52:43Z","publisher":"American Mathematical Society (AMS)","doi":"10.1090/mcom/3672","title":"Spanning the isogeny class of a power of an elliptic curve","issue":"333","publication_status":"published","publication_identifier":{"issn":["0025-5718","1088-6842"]},"citation":{"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>","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>.","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>.","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} }","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","year":"2021"},{"language":[{"iso":"eng"}],"_id":"55288","user_id":"106108","department":[{"_id":"102"}],"status":"public","type":"journal_article","publication":"J. 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Modular hyperbolas and Beatty sequences. <i>J Number Theory</i>. 2020;208:148–167. doi:<a href=\"https://doi.org/10.1016/j.jnt.2019.07.022\">10.1016/j.jnt.2019.07.022</a>","ieee":"M. Technau, “Modular hyperbolas and Beatty sequences,” <i>J. Number Theory</i>, vol. 208, pp. 148–167, 2020, doi: <a href=\"https://doi.org/10.1016/j.jnt.2019.07.022\">10.1016/j.jnt.2019.07.022</a>.","chicago":"Technau, Marc. “Modular Hyperbolas and Beatty Sequences.” <i>J. Number Theory</i> 208 (2020): 148–167. <a href=\"https://doi.org/10.1016/j.jnt.2019.07.022\">https://doi.org/10.1016/j.jnt.2019.07.022</a>.","apa":"Technau, M. (2020). Modular hyperbolas and Beatty sequences. <i>J. Number Theory</i>, <i>208</i>, 148–167. <a href=\"https://doi.org/10.1016/j.jnt.2019.07.022\">https://doi.org/10.1016/j.jnt.2019.07.022</a>","mla":"Technau, Marc. “Modular Hyperbolas and Beatty Sequences.” <i>J. 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E., and Marc Technau. “Kloosterman Sums with Twice-Differentiable Functions.” <i>Funct. Approximatio, Comment. Math.</i> 63, no. 1 (2020): 113–124. <a href=\"https://doi.org/10.7169/facm/1845\">https://doi.org/10.7169/facm/1845</a>.","apa":"Shparlinski, I. E., &#38; Technau, M. (2020). Kloosterman sums with twice-differentiable functions. <i>Funct. Approximatio, Comment. Math.</i>, <i>63</i>(1), 113–124. <a href=\"https://doi.org/10.7169/facm/1845\">https://doi.org/10.7169/facm/1845</a>","mla":"Shparlinski, I. E., and Marc Technau. “Kloosterman Sums with Twice-Differentiable Functions.” <i>Funct. Approximatio, Comment. Math.</i>, vol. 63, no. 1, 2020, pp. 113–124, doi:<a href=\"https://doi.org/10.7169/facm/1845\">10.7169/facm/1845</a>.","bibtex":"@article{Shparlinski_Technau_2020, title={Kloosterman sums with twice-differentiable functions}, volume={63}, DOI={<a href=\"https://doi.org/10.7169/facm/1845\">10.7169/facm/1845</a>}, number={1}, journal={Funct. Approximatio, Comment. Math.}, author={Shparlinski, I. E. and Technau, Marc}, year={2020}, pages={113–124} }","short":"I.E. Shparlinski, M. Technau, Funct. Approximatio, Comment. Math. 63 (2020) 113–124."},"year":"2020","issue":"1"},{"author":[{"first_name":"D.","last_name":"Barth","full_name":"Barth, D."},{"last_name":"Beck","full_name":"Beck, M.","first_name":"M."},{"last_name":"Dose","full_name":"Dose, T.","first_name":"T."},{"first_name":"Ch.","full_name":"Glaßer, Ch.","last_name":"Glaßer"},{"full_name":"Michler, L.","last_name":"Michler","first_name":"L."},{"id":"106108","full_name":"Technau, Marc","orcid":"0000-0001-9650-2459","last_name":"Technau","first_name":"Marc"}],"date_created":"2024-07-16T11:09:02Z","volume":"824-825","date_updated":"2024-07-24T07:25:29Z","doi":"10.1016/j.tcs.2020.03.023","title":"Emptiness problems for integer circuits","citation":{"ama":"Barth D, Beck M, Dose T, Glaßer Ch, Michler L, Technau M. Emptiness problems for integer circuits. <i>Theoretical Computer Science</i>. 2020;824-825:11–35. doi:<a href=\"https://doi.org/10.1016/j.tcs.2020.03.023\">10.1016/j.tcs.2020.03.023</a>","chicago":"Barth, D., M. Beck, T. Dose, Ch. Glaßer, L. Michler, and Marc Technau. “Emptiness Problems for Integer Circuits.” <i>Theoretical Computer Science</i> 824–825 (2020): 11–35. <a href=\"https://doi.org/10.1016/j.tcs.2020.03.023\">https://doi.org/10.1016/j.tcs.2020.03.023</a>.","ieee":"D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, and M. Technau, “Emptiness problems for integer circuits,” <i>Theoretical Computer Science</i>, vol. 824–825, pp. 11–35, 2020, doi: <a href=\"https://doi.org/10.1016/j.tcs.2020.03.023\">10.1016/j.tcs.2020.03.023</a>.","apa":"Barth, D., Beck, M., Dose, T., Glaßer, Ch., Michler, L., &#38; Technau, M. (2020). Emptiness problems for integer circuits. <i>Theoretical Computer Science</i>, <i>824–825</i>, 11–35. <a href=\"https://doi.org/10.1016/j.tcs.2020.03.023\">https://doi.org/10.1016/j.tcs.2020.03.023</a>","bibtex":"@article{Barth_Beck_Dose_Glaßer_Michler_Technau_2020, title={Emptiness problems for integer circuits}, volume={824–825}, DOI={<a href=\"https://doi.org/10.1016/j.tcs.2020.03.023\">10.1016/j.tcs.2020.03.023</a>}, journal={Theoretical Computer Science}, author={Barth, D. and Beck, M. and Dose, T. and Glaßer, Ch. and Michler, L. and Technau, Marc}, year={2020}, pages={11–35} }","mla":"Barth, D., et al. “Emptiness Problems for Integer Circuits.” <i>Theoretical Computer Science</i>, vol. 824–825, 2020, pp. 11–35, doi:<a href=\"https://doi.org/10.1016/j.tcs.2020.03.023\">10.1016/j.tcs.2020.03.023</a>.","short":"D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, M. Technau, Theoretical Computer Science 824–825 (2020) 11–35."},"page":"11–35","year":"2020","user_id":"106108","department":[{"_id":"102"}],"_id":"55283","extern":"1","language":[{"iso":"eng"}],"type":"journal_article","publication":"Theoretical Computer Science","status":"public"},{"doi":"10.4064/aa180220-20-3","date_updated":"2023-03-06T10:19:53Z","volume":193,"author":[{"full_name":"Elsenhans, Andreas-Stephan","last_name":"Elsenhans","first_name":"Andreas-Stephan"},{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"},{"first_name":"Florin","full_name":"Nicolae, Florin","last_name":"Nicolae"}],"page":"217-233","intvolume":"       193","citation":{"ama":"Elsenhans A-S, Klüners J, Nicolae F. Imaginary quadratic number fields with class groups of small exponent. <i>Acta Arithmetica</i>. 2020;193(3):217-233. doi:<a href=\"https://doi.org/10.4064/aa180220-20-3\">10.4064/aa180220-20-3</a>","chicago":"Elsenhans, Andreas-Stephan, Jürgen Klüners, and Florin Nicolae. “Imaginary Quadratic Number Fields with Class Groups of Small Exponent.” <i>Acta Arithmetica</i> 193, no. 3 (2020): 217–33. <a href=\"https://doi.org/10.4064/aa180220-20-3\">https://doi.org/10.4064/aa180220-20-3</a>.","ieee":"A.-S. Elsenhans, J. Klüners, and F. Nicolae, “Imaginary quadratic number fields with class groups of small exponent,” <i>Acta Arithmetica</i>, vol. 193, no. 3, pp. 217–233, 2020, doi: <a href=\"https://doi.org/10.4064/aa180220-20-3\">10.4064/aa180220-20-3</a>.","apa":"Elsenhans, A.-S., Klüners, J., &#38; Nicolae, F. (2020). Imaginary quadratic number fields with class groups of small exponent. <i>Acta Arithmetica</i>, <i>193</i>(3), 217–233. <a href=\"https://doi.org/10.4064/aa180220-20-3\">https://doi.org/10.4064/aa180220-20-3</a>","bibtex":"@article{Elsenhans_Klüners_Nicolae_2020, title={Imaginary quadratic number fields with class groups of small exponent}, volume={193}, DOI={<a href=\"https://doi.org/10.4064/aa180220-20-3\">10.4064/aa180220-20-3</a>}, number={3}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish Academy of Sciences}, author={Elsenhans, Andreas-Stephan and Klüners, Jürgen and Nicolae, Florin}, year={2020}, pages={217–233} }","short":"A.-S. Elsenhans, J. Klüners, F. Nicolae, Acta Arithmetica 193 (2020) 217–233.","mla":"Elsenhans, Andreas-Stephan, et al. “Imaginary Quadratic Number Fields with Class Groups of Small Exponent.” <i>Acta Arithmetica</i>, vol. 193, no. 3, Institute of Mathematics, Polish Academy of Sciences, 2020, pp. 217–33, doi:<a href=\"https://doi.org/10.4064/aa180220-20-3\">10.4064/aa180220-20-3</a>."},"publication_identifier":{"issn":["0065-1036","1730-6264"]},"publication_status":"published","_id":"34842","department":[{"_id":"102"}],"user_id":"93826","status":"public","type":"journal_article","title":"Imaginary quadratic number fields with class groups of small exponent","publisher":"Institute of Mathematics, Polish Academy of Sciences","date_created":"2022-12-22T10:51:13Z","year":"2020","issue":"3","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["1803.02056 "]},"abstract":[{"lang":"eng","text":"Let D<0 be a fundamental discriminant and denote by E(D) the exponent of the ideal class group Cl(D) of K=ℚ(√D). Under the assumption that no Siegel zeros exist we compute all such D with E(D) dividing 8. We compute all D with |D| ≤ 3.1⋅10²⁰ such that E(D) ≤ 8."}],"publication":"Acta Arithmetica"},{"doi":"10.1016/j.jnt.2019.11.007","volume":212,"author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"},{"full_name":"Müller, Raphael","last_name":"Müller","first_name":"Raphael"}],"date_updated":"2025-06-13T08:18:30Z","intvolume":"       212","page":"311-322","citation":{"bibtex":"@article{Klüners_Müller_2020, title={The conductor density of local function fields with abelian Galois group}, volume={212}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2019.11.007\">10.1016/j.jnt.2019.11.007</a>}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Klüners, Jürgen and Müller, Raphael}, year={2020}, pages={311–322} }","short":"J. Klüners, R. Müller, Journal of Number Theory 212 (2020) 311–322.","mla":"Klüners, Jürgen, and Raphael Müller. “The Conductor Density of Local Function Fields with Abelian Galois Group.” <i>Journal of Number Theory</i>, vol. 212, Elsevier BV, 2020, pp. 311–22, doi:<a href=\"https://doi.org/10.1016/j.jnt.2019.11.007\">10.1016/j.jnt.2019.11.007</a>.","apa":"Klüners, J., &#38; Müller, R. (2020). The conductor density of local function fields with abelian Galois group. <i>Journal of Number Theory</i>, <i>212</i>, 311–322. <a href=\"https://doi.org/10.1016/j.jnt.2019.11.007\">https://doi.org/10.1016/j.jnt.2019.11.007</a>","ama":"Klüners J, Müller R. The conductor density of local function fields with abelian Galois group. <i>Journal of Number Theory</i>. 2020;212:311-322. doi:<a href=\"https://doi.org/10.1016/j.jnt.2019.11.007\">10.1016/j.jnt.2019.11.007</a>","chicago":"Klüners, Jürgen, and Raphael Müller. “The Conductor Density of Local Function Fields with Abelian Galois Group.” <i>Journal of Number Theory</i> 212 (2020): 311–22. <a href=\"https://doi.org/10.1016/j.jnt.2019.11.007\">https://doi.org/10.1016/j.jnt.2019.11.007</a>.","ieee":"J. Klüners and R. Müller, “The conductor density of local function fields with abelian Galois group,” <i>Journal of Number Theory</i>, vol. 212, pp. 311–322, 2020, doi: <a href=\"https://doi.org/10.1016/j.jnt.2019.11.007\">10.1016/j.jnt.2019.11.007</a>."},"publication_identifier":{"issn":["0022-314X"]},"publication_status":"published","department":[{"_id":"102"}],"user_id":"82981","_id":"34841","status":"public","type":"journal_article","title":"The conductor density of local function fields with abelian Galois group","date_created":"2022-12-22T10:50:03Z","publisher":"Elsevier BV","year":"2020","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"external_id":{"arxiv":["1904.02573 "]},"abstract":[{"lang":"eng","text":"We give an exact formula for the number of G-extensions of local function fields Fq((t)) for finite abelian groups G up to a conductor bound. As an application we give a lower bound for the corresponding counting problem by discriminant.\r\n"}],"publication":"Journal of Number Theory"},{"doi":"10.1142/s1793042119500131","title":"Quaternary quadratic lattices over number fields","volume":15,"author":[{"full_name":"Kirschmer, Markus","id":"82258","last_name":"Kirschmer","first_name":"Markus"},{"last_name":"Nebe","full_name":"Nebe, Gabriele","first_name":"Gabriele"}],"date_created":"2022-12-23T11:05:09Z","date_updated":"2023-12-06T10:05:59Z","publisher":"World Scientific Pub Co Pte Lt","intvolume":"        15","page":"309-325","citation":{"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>.","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>.","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>","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>","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} }","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>.","short":"M. Kirschmer, G. Nebe, International Journal of Number Theory 15 (2019) 309–325."},"year":"2019","issue":"02","publication_identifier":{"issn":["1793-0421","1793-7310"]},"publication_status":"published","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"department":[{"_id":"102"}],"user_id":"82258","_id":"34917","status":"public","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"}],"publication":"International Journal of Number Theory","type":"journal_article"}]