[{"author":[{"first_name":"Markus","id":"82258","full_name":"Kirschmer, Markus","last_name":"Kirschmer"}],"date_created":"2023-03-07T08:27:36Z","volume":30,"date_updated":"2023-04-04T09:07:32Z","publisher":"Cellule MathDoc/CEDRAM","doi":"10.5802/jtnb.1052","title":"One-class genera of exceptional groups over number fields","issue":"3","publication_status":"published","publication_identifier":{"issn":["1246-7405","2118-8572"]},"citation":{"bibtex":"@article{Kirschmer_2018, title={One-class genera of exceptional groups over number fields}, volume={30}, DOI={<a href=\"https://doi.org/10.5802/jtnb.1052\">10.5802/jtnb.1052</a>}, number={3}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule MathDoc/CEDRAM}, author={Kirschmer, Markus}, year={2018}, pages={847–857} }","mla":"Kirschmer, Markus. “One-Class Genera of Exceptional Groups over Number Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i>, vol. 30, no. 3, Cellule MathDoc/CEDRAM, 2018, pp. 847–57, doi:<a href=\"https://doi.org/10.5802/jtnb.1052\">10.5802/jtnb.1052</a>.","short":"M. Kirschmer, Journal de Théorie Des Nombres de Bordeaux 30 (2018) 847–857.","apa":"Kirschmer, M. (2018). One-class genera of exceptional groups over number fields. <i>Journal de Théorie Des Nombres de Bordeaux</i>, <i>30</i>(3), 847–857. <a href=\"https://doi.org/10.5802/jtnb.1052\">https://doi.org/10.5802/jtnb.1052</a>","chicago":"Kirschmer, Markus. “One-Class Genera of Exceptional Groups over Number Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i> 30, no. 3 (2018): 847–57. <a href=\"https://doi.org/10.5802/jtnb.1052\">https://doi.org/10.5802/jtnb.1052</a>.","ieee":"M. Kirschmer, “One-class genera of exceptional groups over number fields,” <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 30, no. 3, pp. 847–857, 2018, doi: <a href=\"https://doi.org/10.5802/jtnb.1052\">10.5802/jtnb.1052</a>.","ama":"Kirschmer M. One-class genera of exceptional groups over number fields. <i>Journal de Théorie des Nombres de Bordeaux</i>. 2018;30(3):847-857. doi:<a href=\"https://doi.org/10.5802/jtnb.1052\">10.5802/jtnb.1052</a>"},"intvolume":"        30","page":"847-857","year":"2018","user_id":"93826","department":[{"_id":"102"}],"_id":"42790","language":[{"iso":"eng"}],"extern":"1","keyword":["Algebra and Number Theory"],"type":"journal_article","publication":"Journal de Théorie des Nombres de Bordeaux","status":"public","abstract":[{"lang":"eng","text":"We show that exceptional algebraic groups over number fields do not admit one-class genera of parahoric groups, except in the case G₂ . For the group G₂, we enumerate all such one-class genera for the usual seven-dimensional representation."}]},{"doi":"10.5802/jtnb.655","date_updated":"2023-03-06T09:09:56Z","volume":21,"author":[{"last_name":"Belabas","full_name":"Belabas, Karim","first_name":"Karim"},{"last_name":"van Hoeij","full_name":"van Hoeij, Mark","first_name":"Mark"},{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"},{"first_name":"Allan","full_name":"Steel, Allan","last_name":"Steel"}],"intvolume":"        21","page":"15-39","citation":{"ieee":"K. Belabas, M. van Hoeij, J. Klüners, and A. Steel, “Factoring polynomials over global fields,” <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 21, no. 1, pp. 15–39, 2009, doi: <a href=\"https://doi.org/10.5802/jtnb.655\">10.5802/jtnb.655</a>.","chicago":"Belabas, Karim, Mark van Hoeij, Jürgen Klüners, and Allan Steel. “Factoring Polynomials over Global Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i> 21, no. 1 (2009): 15–39. <a href=\"https://doi.org/10.5802/jtnb.655\">https://doi.org/10.5802/jtnb.655</a>.","ama":"Belabas K, van Hoeij M, Klüners J, Steel A. Factoring polynomials over global fields. <i>Journal de Théorie des Nombres de Bordeaux</i>. 2009;21(1):15-39. doi:<a href=\"https://doi.org/10.5802/jtnb.655\">10.5802/jtnb.655</a>","apa":"Belabas, K., van Hoeij, M., Klüners, J., &#38; Steel, A. (2009). Factoring polynomials over global fields. <i>Journal de Théorie Des Nombres de Bordeaux</i>, <i>21</i>(1), 15–39. <a href=\"https://doi.org/10.5802/jtnb.655\">https://doi.org/10.5802/jtnb.655</a>","short":"K. Belabas, M. van Hoeij, J. Klüners, A. Steel, Journal de Théorie Des Nombres de Bordeaux 21 (2009) 15–39.","mla":"Belabas, Karim, et al. “Factoring Polynomials over Global Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i>, vol. 21, no. 1, Cellule MathDoc/CEDRAM, 2009, pp. 15–39, doi:<a href=\"https://doi.org/10.5802/jtnb.655\">10.5802/jtnb.655</a>.","bibtex":"@article{Belabas_van Hoeij_Klüners_Steel_2009, title={Factoring polynomials over global fields}, volume={21}, DOI={<a href=\"https://doi.org/10.5802/jtnb.655\">10.5802/jtnb.655</a>}, number={1}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule MathDoc/CEDRAM}, author={Belabas, Karim and van Hoeij, Mark and Klüners, Jürgen and Steel, Allan}, year={2009}, pages={15–39} }"},"publication_identifier":{"issn":["1246-7405"]},"publication_status":"published","_id":"34889","department":[{"_id":"102"}],"user_id":"93826","status":"public","type":"journal_article","title":"Factoring polynomials over global fields","publisher":"Cellule MathDoc/CEDRAM","date_created":"2022-12-23T09:33:37Z","year":"2009","issue":"1","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["math/0409510 "]},"abstract":[{"lang":"eng","text":"We prove that van Hoeij’s original algorithm to factor univariate polynomials over the rationals runs in polynomial time, as well as natural variants. In particular, our approach also yields polynomial time complexity results for bivariate polynomials over a finite field."}],"publication":"Journal de Théorie des Nombres de Bordeaux"},{"title":"Asymptotics of number fields and the Cohen–Lenstra heuristics","publisher":"Cellule MathDoc/CEDRAM","date_created":"2022-12-23T09:37:01Z","year":"2006","issue":"3","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["math/0512260 "]},"abstract":[{"lang":"eng","text":"We study the asymptotics conjecture of Malle for dihedral groups Dℓ of order 2ℓ, where ℓ is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen--Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds. "}],"publication":"Journal de Théorie des Nombres de Bordeaux","doi":"10.5802/jtnb.561","date_updated":"2023-03-06T09:12:04Z","author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"}],"volume":18,"citation":{"ama":"Klüners J. Asymptotics of number fields and the Cohen–Lenstra heuristics. <i>Journal de Théorie des Nombres de Bordeaux</i>. 2006;18(3):607-615. doi:<a href=\"https://doi.org/10.5802/jtnb.561\">10.5802/jtnb.561</a>","chicago":"Klüners, Jürgen. “Asymptotics of Number Fields and the Cohen–Lenstra Heuristics.” <i>Journal de Théorie Des Nombres de Bordeaux</i> 18, no. 3 (2006): 607–15. <a href=\"https://doi.org/10.5802/jtnb.561\">https://doi.org/10.5802/jtnb.561</a>.","ieee":"J. Klüners, “Asymptotics of number fields and the Cohen–Lenstra heuristics,” <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 18, no. 3, pp. 607–615, 2006, doi: <a href=\"https://doi.org/10.5802/jtnb.561\">10.5802/jtnb.561</a>.","apa":"Klüners, J. (2006). Asymptotics of number fields and the Cohen–Lenstra heuristics. <i>Journal de Théorie Des Nombres de Bordeaux</i>, <i>18</i>(3), 607–615. <a href=\"https://doi.org/10.5802/jtnb.561\">https://doi.org/10.5802/jtnb.561</a>","bibtex":"@article{Klüners_2006, title={Asymptotics of number fields and the Cohen–Lenstra heuristics}, volume={18}, DOI={<a href=\"https://doi.org/10.5802/jtnb.561\">10.5802/jtnb.561</a>}, number={3}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule MathDoc/CEDRAM}, author={Klüners, Jürgen}, year={2006}, pages={607–615} }","mla":"Klüners, Jürgen. “Asymptotics of Number Fields and the Cohen–Lenstra Heuristics.” <i>Journal de Théorie Des Nombres de Bordeaux</i>, vol. 18, no. 3, Cellule MathDoc/CEDRAM, 2006, pp. 607–15, doi:<a href=\"https://doi.org/10.5802/jtnb.561\">10.5802/jtnb.561</a>.","short":"J. Klüners, Journal de Théorie Des Nombres de Bordeaux 18 (2006) 607–615."},"page":"607-615","intvolume":"        18","publication_status":"published","publication_identifier":{"issn":["1246-7405"]},"_id":"34891","user_id":"93826","department":[{"_id":"102"}],"status":"public","type":"journal_article"}]