[{"date_updated":"2024-07-24T07:23:20Z","intvolume":"      2024","status":"public","year":"2024","title":"On restricted averages of Dedekind sums","author":[{"full_name":"Minelli, P.","first_name":"P.","last_name":"Minelli"},{"first_name":"A.","last_name":"Sourmelidis","full_name":"Sourmelidis, A."},{"id":"106108","last_name":"Technau","first_name":"Marc","orcid":"0000-0001-9650-2459","full_name":"Technau, Marc"}],"doi":"10.1093/imrn/rnad283","user_id":"106108","volume":2024,"page":"8485–8502","language":[{"iso":"eng"}],"_id":"55276","issue":"10","publication":"Int. Math. Res. Not. IMRN","citation":{"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} }","ama":"Minelli P, Sourmelidis A, Technau M. 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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>","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} }","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>","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>."},"publication":"Math. Ann."},{"date_created":"2024-07-16T11:09:01Z","type":"journal_article","department":[{"_id":"102"}],"issue":"3","publication":"Acta Arith.","citation":{"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>.","short":"Ch. Elsholtz, B. Klahn, M. Technau, Acta Arith. 205:3 (2022) 251–263.","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>.","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>","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} }","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>","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>."},"extern":"1","page":"251–263","_id":"55280","language":[{"iso":"eng"}],"doi":"10.4064/aa220407-9-7","user_id":"106108","volume":"205:3","year":"2022","title":"On polynomials with roots modulo almost all primes","status":"public","author":[{"full_name":"Elsholtz, Ch.","last_name":"Elsholtz","first_name":"Ch."},{"full_name":"Klahn, B.","first_name":"B.","last_name":"Klahn"},{"id":"106108","full_name":"Technau, Marc","last_name":"Technau","first_name":"Marc","orcid":"0000-0001-9650-2459"}],"date_updated":"2024-07-24T07:26:22Z"},{"status":"public","user_id":"93826","volume":150,"page":"2793-2805","publisher":"American Mathematical Society (AMS)","_id":"34839","citation":{"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>","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>.","short":"J. Klüners, J. Wang, Proceedings of the American Mathematical Society 150 (2022) 2793–2805.","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>.","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>.","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>","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} }"},"external_id":{"arxiv":["2003.12161 "]},"publication_status":"published","date_updated":"2023-03-06T08:47:42Z","intvolume":"       150","title":"ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group","year":"2022","publication_identifier":{"issn":["0002-9939","1088-6826"]},"author":[{"id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen","last_name":"Klüners"},{"first_name":"Jiuya","last_name":"Wang","full_name":"Wang, Jiuya"}],"doi":"10.1090/proc/15882","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","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."}],"issue":"7","publication":"Proceedings of the American Mathematical Society","keyword":["Applied Mathematics","General Mathematics"],"type":"journal_article","department":[{"_id":"102"}],"date_created":"2022-12-22T10:47:01Z"},{"keyword":["Algebra and Number Theory"],"type":"journal_article","department":[{"_id":"102"}],"date_created":"2022-12-22T10:08:23Z","abstract":[{"lang":"eng","text":"We prove an upper bound for the asymptotics of counting functions of number fields with nilpotent Galois groups. "}],"issue":"2","publication":"Acta Arithmetica","doi":"10.4064/aa211207-16-5","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-03-06T08:48:33Z","intvolume":"       204","year":"2022","title":"The asymptotics of nilpotent Galois groups","author":[{"last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202"}],"publication_identifier":{"issn":["0065-1036","1730-6264"]},"external_id":{"arxiv":["2011.04325 "]},"citation":{"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>.","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>","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>.","short":"J. Klüners, Acta Arithmetica 204 (2022) 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>.","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} }","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>"},"user_id":"93826","volume":204,"page":"165-184","publisher":"Institute of Mathematics, Polish Academy of Sciences","_id":"34835","status":"public"},{"status":"public","_id":"45854","publisher":"Informa UK Limited","page":"280-301","volume":31,"user_id":"93826","citation":{"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>","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} }","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>.","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>.","short":"M. Kirschmer, G. Nebe, Experimental Mathematics 31 (2022) 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>","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>."},"author":[{"full_name":"Kirschmer, Markus","first_name":"Markus","last_name":"Kirschmer","id":"82258"},{"full_name":"Nebe, Gabriele","last_name":"Nebe","first_name":"Gabriele"}],"publication_identifier":{"issn":["1058-6458","1944-950X"]},"title":"Binary Hermitian Lattices over Number Fields","year":"2022","intvolume":"        31","publication_status":"published","date_updated":"2023-07-04T08:29:22Z","language":[{"iso":"eng"}],"doi":"10.1080/10586458.2019.1618756","issue":"1","publication":"Experimental Mathematics","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"}],"date_created":"2023-07-04T08:28:04Z","department":[{"_id":"102"}],"type":"journal_article","keyword":["General Mathematics"]},{"date_created":"2024-07-16T11:09:03Z","type":"journal_article","department":[{"_id":"102"}],"issue":"2","publication":"Unif. Distrib. Theory","citation":{"apa":"Baier, St., Mazumder, D., &#38; Technau, M. (2021). On the distribution of αp modulo one in quadratic number fields. <i>Unif. Distrib. Theory</i>, <i>16</i>(2), 1–48. <a href=\"https://doi.org/10.2478/udt-2021-0006\">https://doi.org/10.2478/udt-2021-0006</a>","ieee":"St. Baier, D. Mazumder, and M. Technau, “On the distribution of αp modulo one in quadratic number fields,” <i>Unif. Distrib. Theory</i>, vol. 16, no. 2, pp. 1–48, 2021, doi: <a href=\"https://doi.org/10.2478/udt-2021-0006\">10.2478/udt-2021-0006</a>.","short":"St. Baier, D. Mazumder, M. Technau, Unif. Distrib. Theory 16 (2021) 1–48.","chicago":"Baier, St., D. Mazumder, and Marc Technau. “On the Distribution of Αp modulo One in Quadratic Number Fields.” <i>Unif. Distrib. Theory</i> 16, no. 2 (2021): 1–48. <a href=\"https://doi.org/10.2478/udt-2021-0006\">https://doi.org/10.2478/udt-2021-0006</a>.","mla":"Baier, St., et al. “On the Distribution of Αp modulo One in Quadratic Number Fields.” <i>Unif. Distrib. Theory</i>, vol. 16, no. 2, 2021, pp. 1–48, doi:<a href=\"https://doi.org/10.2478/udt-2021-0006\">10.2478/udt-2021-0006</a>.","ama":"Baier St, Mazumder D, Technau M. On the distribution of αp modulo one in quadratic number fields. <i>Unif Distrib Theory</i>. 2021;16(2):1–48. doi:<a href=\"https://doi.org/10.2478/udt-2021-0006\">10.2478/udt-2021-0006</a>","bibtex":"@article{Baier_Mazumder_Technau_2021, title={On the distribution of αp modulo one in quadratic number fields}, volume={16}, DOI={<a href=\"https://doi.org/10.2478/udt-2021-0006\">10.2478/udt-2021-0006</a>}, number={2}, journal={Unif. Distrib. Theory}, author={Baier, St. and Mazumder, D. and Technau, Marc}, year={2021}, pages={1–48} }"},"extern":"1","page":"1–48","_id":"55290","language":[{"iso":"eng"}],"doi":"10.2478/udt-2021-0006","user_id":"106108","volume":16,"title":"On the distribution of αp modulo one in quadratic number fields","year":"2021","status":"public","author":[{"last_name":"Baier","first_name":"St.","full_name":"Baier, St."},{"full_name":"Mazumder, D.","first_name":"D.","last_name":"Mazumder"},{"id":"106108","full_name":"Technau, Marc","first_name":"Marc","last_name":"Technau","orcid":"0000-0001-9650-2459"}],"date_updated":"2024-07-24T07:23:43Z","intvolume":"        16"},{"extern":"1","publication":"Acta Arith.","issue":"1","citation":{"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>","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} }","mla":"Technau, Marc, and A. 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>.","short":"M. Technau, A. Zafeiropoulos, Acta Arith. 197 (2021) 93–104.","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>.","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>","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>."},"type":"journal_article","department":[{"_id":"102"}],"date_created":"2024-07-16T11:09:03Z","date_updated":"2024-07-24T07:25:48Z","intvolume":"       197","title":"Metric results on summatory arithmetic functions on Beatty sets","year":"2021","status":"public","author":[{"id":"106108","full_name":"Technau, Marc","orcid":"0000-0001-9650-2459","last_name":"Technau","first_name":"Marc"},{"first_name":"A.","last_name":"Zafeiropoulos","full_name":"Zafeiropoulos, A."}],"doi":"10.4064/aa200128-10-6","user_id":"106108","volume":197,"page":"93–104","language":[{"iso":"eng"}],"_id":"55289"},{"citation":{"apa":"Klüners, J., &#38; Komatsu, T. (2021). Imaginary multiquadratic number fields with class group of exponent $3$ and $5$. <i>Mathematics of Computation</i>, <i>90</i>(329), 1483–1497. <a href=\"https://doi.org/10.1090/mcom/3609\">https://doi.org/10.1090/mcom/3609</a>","ieee":"J. Klüners and T. Komatsu, “Imaginary multiquadratic number fields with class group of exponent $3$ and $5$,” <i>Mathematics of Computation</i>, vol. 90, no. 329, pp. 1483–1497, 2021, doi: <a href=\"https://doi.org/10.1090/mcom/3609\">10.1090/mcom/3609</a>.","short":"J. Klüners, T. Komatsu, Mathematics of Computation 90 (2021) 1483–1497.","chicago":"Klüners, Jürgen, and Toru Komatsu. “Imaginary Multiquadratic Number Fields with Class Group of Exponent $3$ and $5$.” <i>Mathematics of Computation</i> 90, no. 329 (2021): 1483–97. <a href=\"https://doi.org/10.1090/mcom/3609\">https://doi.org/10.1090/mcom/3609</a>.","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>.","ama":"Klüners J, Komatsu T. Imaginary multiquadratic number fields with class group of exponent $3$ and $5$. <i>Mathematics of Computation</i>. 2021;90(329):1483-1497. 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} }"},"external_id":{"arxiv":["2004.03308v2"]},"status":"public","user_id":"93826","volume":90,"page":"1483-1497","_id":"34840","publisher":"American Mathematical Society (AMS)","abstract":[{"text":"In this paper we obtain a complete list of imaginary n-quadratic fields with class groups of exponent 3 and 5 under ERH for every positive integer n where an n-quadratic field is a number field of degree 2ⁿ represented as the composite of n quadratic fields. ","lang":"eng"}],"publication":"Mathematics of Computation","issue":"329","keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"type":"journal_article","department":[{"_id":"102"}],"date_created":"2022-12-22T10:48:44Z","date_updated":"2023-03-06T08:57:45Z","publication_status":"published","intvolume":"        90","title":"Imaginary multiquadratic number fields with class group of exponent $3$ and $5$","year":"2021","publication_identifier":{"issn":["0025-5718","1088-6842"]},"author":[{"last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202"},{"last_name":"Komatsu","first_name":"Toru","full_name":"Komatsu, Toru"}],"doi":"10.1090/mcom/3609","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"doi":"10.1090/mcom/3672","year":"2021","title":"Spanning the isogeny class of a power of an elliptic curve","author":[{"id":"82258","full_name":"Kirschmer, Markus","first_name":"Markus","last_name":"Kirschmer"},{"last_name":"Narbonne","first_name":"Fabien","full_name":"Narbonne, Fabien"},{"full_name":"Ritzenthaler, Christophe","last_name":"Ritzenthaler","first_name":"Christophe"},{"full_name":"Robert, Damien","last_name":"Robert","first_name":"Damien"}],"publication_identifier":{"issn":["0025-5718","1088-6842"]},"publication_status":"published","date_updated":"2023-04-04T07:52:43Z","intvolume":"        91","date_created":"2022-12-23T11:02:02Z","type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"department":[{"_id":"102"}],"issue":"333","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"}],"page":"401-449","_id":"34912","publisher":"American Mathematical Society (AMS)","user_id":"93826","volume":91,"status":"public","citation":{"short":"M. Kirschmer, F. Narbonne, C. Ritzenthaler, D. Robert, Mathematics of Computation 91 (2021) 401–449.","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>.","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>.","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>","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} }","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>","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>."}},{"author":[{"full_name":"Baier, St.","first_name":"St.","last_name":"Baier"},{"first_name":"Marc","orcid":"0000-0001-9650-2459","last_name":"Technau","full_name":"Technau, Marc","id":"106108"}],"year":"2020","status":"public","title":"On the distribution of αp modulo one in imaginary quadratic number fields with class number one","intvolume":"        32","date_updated":"2024-07-24T07:23:57Z","language":[{"iso":"eng"}],"_id":"55288","page":"719–760","volume":32,"doi":"10.5802/jtnb.1141","user_id":"106108","citation":{"chicago":"Baier, St., and Marc Technau. “On the Distribution of Αp modulo One in Imaginary Quadratic Number Fields with Class Number One.” <i>J. Théor. Nombres Bordx.</i> 32, no. 2 (2020): 719–760. <a href=\"https://doi.org/10.5802/jtnb.1141\">https://doi.org/10.5802/jtnb.1141</a>.","short":"St. Baier, M. Technau, J. Théor. Nombres Bordx. 32 (2020) 719–760.","apa":"Baier, St., &#38; Technau, M. (2020). On the distribution of αp modulo one in imaginary quadratic number fields with class number one. <i>J. Théor. Nombres Bordx.</i>, <i>32</i>(2), 719–760. <a href=\"https://doi.org/10.5802/jtnb.1141\">https://doi.org/10.5802/jtnb.1141</a>","ieee":"St. Baier and M. Technau, “On the distribution of αp modulo one in imaginary quadratic number fields with class number one,” <i>J. Théor. Nombres Bordx.</i>, vol. 32, no. 2, pp. 719–760, 2020, doi: <a href=\"https://doi.org/10.5802/jtnb.1141\">10.5802/jtnb.1141</a>.","ama":"Baier St, Technau M. On the distribution of αp modulo one in imaginary quadratic number fields with class number one. <i>J Théor Nombres Bordx</i>. 2020;32(2):719–760. doi:<a href=\"https://doi.org/10.5802/jtnb.1141\">10.5802/jtnb.1141</a>","bibtex":"@article{Baier_Technau_2020, title={On the distribution of αp modulo one in imaginary quadratic number fields with class number one}, volume={32}, DOI={<a href=\"https://doi.org/10.5802/jtnb.1141\">10.5802/jtnb.1141</a>}, number={2}, journal={J. Théor. Nombres Bordx.}, author={Baier, St. and Technau, Marc}, year={2020}, pages={719–760} }","mla":"Baier, St., and Marc Technau. “On the Distribution of Αp modulo One in Imaginary Quadratic Number Fields with Class Number One.” <i>J. Théor. Nombres Bordx.</i>, vol. 32, no. 2, 2020, pp. 719–760, doi:<a href=\"https://doi.org/10.5802/jtnb.1141\">10.5802/jtnb.1141</a>."},"issue":"2","publication":"J. Théor. Nombres Bordx.","date_created":"2024-07-16T11:09:02Z","department":[{"_id":"102"}],"type":"journal_article"},{"status":"public","title":"Modular hyperbolas and Beatty sequences","year":"2020","author":[{"id":"106108","orcid":"0000-0001-9650-2459","last_name":"Technau","first_name":"Marc","full_name":"Technau, Marc"}],"date_updated":"2024-07-24T07:24:11Z","intvolume":"       208","page":"148–167","language":[{"iso":"eng"}],"_id":"55286","doi":"10.1016/j.jnt.2019.07.022","user_id":"106108","volume":208,"publication":"J. Number Theory","citation":{"bibtex":"@article{Technau_2020, title={Modular hyperbolas and Beatty sequences}, volume={208}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2019.07.022\">10.1016/j.jnt.2019.07.022</a>}, journal={J. Number Theory}, author={Technau, Marc}, year={2020}, pages={148–167} }","ama":"Technau M. 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>","mla":"Technau, Marc. “Modular Hyperbolas and Beatty Sequences.” <i>J. Number Theory</i>, vol. 208, 2020, pp. 148–167, 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>.","short":"M. Technau, J. Number Theory 208 (2020) 148–167.","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>.","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>"},"extern":"1","date_created":"2024-07-16T11:09:02Z","type":"journal_article","department":[{"_id":"102"}]},{"department":[{"_id":"102"}],"type":"journal_article","date_created":"2024-07-16T11:09:02Z","extern":"1","citation":{"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>.","ama":"Shparlinski IE, Technau M. Kloosterman sums with twice-differentiable functions. <i>Funct Approximatio, Comment Math</i>. 2020;63(1):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} }","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>","ieee":"I. E. Shparlinski and M. Technau, “Kloosterman sums with twice-differentiable functions,” <i>Funct. Approximatio, Comment. Math.</i>, vol. 63, no. 1, pp. 113–124, 2020, doi: <a href=\"https://doi.org/10.7169/facm/1845\">10.7169/facm/1845</a>.","chicago":"Shparlinski, I. 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>.","short":"I.E. Shparlinski, M. Technau, Funct. Approximatio, Comment. Math. 63 (2020) 113–124."},"publication":"Funct. Approximatio, Comment. Math.","issue":"1","volume":63,"user_id":"106108","doi":"10.7169/facm/1845","language":[{"iso":"eng"}],"_id":"55287","page":"113–124","intvolume":"        63","date_updated":"2024-07-24T07:25:54Z","author":[{"last_name":"Shparlinski","first_name":"I. E.","full_name":"Shparlinski, I. E."},{"id":"106108","full_name":"Technau, Marc","orcid":"0000-0001-9650-2459","last_name":"Technau","first_name":"Marc"}],"year":"2020","status":"public","title":"Kloosterman sums with twice-differentiable functions"},{"author":[{"full_name":"Barth, D.","last_name":"Barth","first_name":"D."},{"full_name":"Beck, M.","last_name":"Beck","first_name":"M."},{"last_name":"Dose","first_name":"T.","full_name":"Dose, T."},{"last_name":"Glaßer","first_name":"Ch.","full_name":"Glaßer, Ch."},{"full_name":"Michler, L.","first_name":"L.","last_name":"Michler"},{"orcid":"0000-0001-9650-2459","last_name":"Technau","first_name":"Marc","full_name":"Technau, Marc","id":"106108"}],"year":"2020","status":"public","title":"Emptiness problems for integer circuits","date_updated":"2024-07-24T07:25:29Z","_id":"55283","language":[{"iso":"eng"}],"page":"11–35","volume":"824-825","user_id":"106108","doi":"10.1016/j.tcs.2020.03.023","citation":{"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>","short":"D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, M. Technau, Theoretical Computer Science 824–825 (2020) 11–35.","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>.","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>.","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} }","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>"},"publication":"Theoretical Computer Science","extern":"1","date_created":"2024-07-16T11:09:02Z","department":[{"_id":"102"}],"type":"journal_article"},{"date_created":"2022-12-22T10:51:13Z","type":"journal_article","keyword":["Algebra and Number Theory"],"department":[{"_id":"102"}],"publication":"Acta Arithmetica","issue":"3","abstract":[{"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.","lang":"eng"}],"language":[{"iso":"eng"}],"doi":"10.4064/aa180220-20-3","year":"2020","title":"Imaginary quadratic number fields with class groups of small exponent","publication_identifier":{"issn":["0065-1036","1730-6264"]},"author":[{"last_name":"Elsenhans","first_name":"Andreas-Stephan","full_name":"Elsenhans, Andreas-Stephan"},{"id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen"},{"full_name":"Nicolae, Florin","last_name":"Nicolae","first_name":"Florin"}],"date_updated":"2023-03-06T10:19:53Z","publication_status":"published","intvolume":"       193","external_id":{"arxiv":["1803.02056 "]},"citation":{"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} }","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>","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>.","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>.","short":"A.-S. Elsenhans, J. Klüners, F. Nicolae, Acta Arithmetica 193 (2020) 217–233.","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>"},"page":"217-233","_id":"34842","publisher":"Institute of Mathematics, Polish Academy of Sciences","user_id":"93826","volume":193,"status":"public"},{"publication_status":"published","date_updated":"2025-06-13T08:18:30Z","intvolume":"       212","title":"The conductor density of local function fields with abelian Galois group","year":"2020","publication_identifier":{"issn":["0022-314X"]},"author":[{"id":"21202","first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen"},{"full_name":"Müller, Raphael","last_name":"Müller","first_name":"Raphael"}],"doi":"10.1016/j.jnt.2019.11.007","language":[{"iso":"eng"}],"abstract":[{"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","lang":"eng"}],"publication":"Journal of Number Theory","keyword":["Algebra and Number Theory"],"type":"journal_article","department":[{"_id":"102"}],"date_created":"2022-12-22T10:50:03Z","status":"public","user_id":"82981","volume":212,"page":"311-322","_id":"34841","publisher":"Elsevier BV","citation":{"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>.","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} }","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>","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>.","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>","short":"J. Klüners, R. Müller, Journal of Number Theory 212 (2020) 311–322.","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>."},"external_id":{"arxiv":["1904.02573 "]}},{"citation":{"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>","short":"M. Kirschmer, G. Nebe, International Journal of Number Theory 15 (2019) 309–325.","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} }","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>.","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>."},"page":"309-325","publisher":"World Scientific Pub Co Pte Lt","_id":"34917","user_id":"82258","volume":15,"status":"public","date_created":"2022-12-23T11:05:09Z","type":"journal_article","keyword":["Algebra and Number Theory"],"department":[{"_id":"102"}],"publication":"International Journal of Number Theory","issue":"02","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"}],"language":[{"iso":"eng"}],"doi":"10.1142/s1793042119500131","title":"Quaternary quadratic lattices over number fields","year":"2019","publication_identifier":{"issn":["1793-0421","1793-7310"]},"author":[{"id":"82258","last_name":"Kirschmer","first_name":"Markus","full_name":"Kirschmer, Markus"},{"first_name":"Gabriele","last_name":"Nebe","full_name":"Nebe, Gabriele"}],"publication_status":"published","date_updated":"2023-12-06T10:05:59Z","intvolume":"        15"}]