[{"publication":"Acta Arithmetica","issue":"2","abstract":[{"lang":"eng","text":"We prove an upper bound for the asymptotics of counting functions of number fields with nilpotent Galois groups. "}],"date_created":"2022-12-22T10:08:23Z","department":[{"_id":"102"}],"keyword":["Algebra and Number Theory"],"type":"journal_article","publication_identifier":{"issn":["0065-1036","1730-6264"]},"author":[{"first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202"}],"year":"2022","title":"The asymptotics of nilpotent Galois groups","intvolume":"       204","date_updated":"2023-03-06T08:48:33Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.4064/aa211207-16-5","citation":{"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>.","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>","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} }","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>","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>.","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."},"external_id":{"arxiv":["2011.04325 "]},"status":"public","publisher":"Institute of Mathematics, Polish Academy of Sciences","_id":"34835","page":"165-184","volume":204,"user_id":"93826"},{"status":"public","page":"217-233","_id":"34842","publisher":"Institute of Mathematics, Polish Academy of Sciences","user_id":"93826","volume":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>","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} }","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>.","short":"A.-S. Elsenhans, J. Klüners, F. Nicolae, Acta Arithmetica 193 (2020) 217–233.","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>.","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>","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>."},"external_id":{"arxiv":["1803.02056 "]},"title":"Imaginary quadratic number fields with class groups of small exponent","year":"2020","author":[{"full_name":"Elsenhans, Andreas-Stephan","first_name":"Andreas-Stephan","last_name":"Elsenhans"},{"id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen","last_name":"Klüners"},{"full_name":"Nicolae, Florin","last_name":"Nicolae","first_name":"Florin"}],"publication_identifier":{"issn":["0065-1036","1730-6264"]},"date_updated":"2023-03-06T10:19:53Z","publication_status":"published","intvolume":"       193","language":[{"iso":"eng"}],"doi":"10.4064/aa180220-20-3","issue":"3","publication":"Acta Arithmetica","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"}],"date_created":"2022-12-22T10:51:13Z","keyword":["Algebra and Number Theory"],"type":"journal_article","department":[{"_id":"102"}]},{"language":[{"iso":"eng"}],"doi":"10.4064/aa122-2-3","title":"The number of S₄-fields with given discriminant","year":"2006","author":[{"full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen","id":"21202"}],"publication_identifier":{"issn":["0065-1036","1730-6264"]},"publication_status":"published","date_updated":"2023-03-06T09:52:41Z","intvolume":"       122","date_created":"2022-12-23T09:40:25Z","keyword":["Algebra and Number Theory"],"type":"journal_article","department":[{"_id":"102"}],"publication":"Acta Arithmetica","issue":"2","abstract":[{"text":"We prove that the number of quartic S4--extensions of the rationals of given discriminant d is $O_\\eps(d^{1/2+\\eps})$ for all $\\eps>0$. For a prime number p we derive that the dimension of the space of octahedral modular forms of weight 1 and conductor p or p² is bounded above by O(p¹/²log(p)²). ","lang":"eng"}],"page":"185-194","_id":"34892","publisher":"Institute of Mathematics, Polish Academy of Sciences","user_id":"93826","volume":122,"status":"public","external_id":{"arxiv":["math/0411484"]},"citation":{"chicago":"Klüners, Jürgen. “The Number of S₄-Fields with given Discriminant.” <i>Acta Arithmetica</i> 122, no. 2 (2006): 185–94. <a href=\"https://doi.org/10.4064/aa122-2-3\">https://doi.org/10.4064/aa122-2-3</a>.","short":"J. Klüners, Acta Arithmetica 122 (2006) 185–194.","ieee":"J. Klüners, “The number of S₄-fields with given discriminant,” <i>Acta Arithmetica</i>, vol. 122, no. 2, pp. 185–194, 2006, doi: <a href=\"https://doi.org/10.4064/aa122-2-3\">10.4064/aa122-2-3</a>.","apa":"Klüners, J. (2006). The number of S₄-fields with given discriminant. <i>Acta Arithmetica</i>, <i>122</i>(2), 185–194. <a href=\"https://doi.org/10.4064/aa122-2-3\">https://doi.org/10.4064/aa122-2-3</a>","bibtex":"@article{Klüners_2006, title={The number of S₄-fields with given discriminant}, volume={122}, DOI={<a href=\"https://doi.org/10.4064/aa122-2-3\">10.4064/aa122-2-3</a>}, number={2}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish Academy of Sciences}, author={Klüners, Jürgen}, year={2006}, pages={185–194} }","ama":"Klüners J. The number of S₄-fields with given discriminant. <i>Acta Arithmetica</i>. 2006;122(2):185-194. doi:<a href=\"https://doi.org/10.4064/aa122-2-3\">10.4064/aa122-2-3</a>","mla":"Klüners, Jürgen. “The Number of S₄-Fields with given Discriminant.” <i>Acta Arithmetica</i>, vol. 122, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2006, pp. 185–94, doi:<a href=\"https://doi.org/10.4064/aa122-2-3\">10.4064/aa122-2-3</a>."}}]