[{"abstract":[{"text":"We prove an upper bound for the asymptotics of counting functions of number fields with nilpotent Galois groups. ","lang":"eng"}],"publication":"Acta Arithmetica","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["2011.04325 "]},"year":"2022","issue":"2","title":"The asymptotics of nilpotent Galois groups","publisher":"Institute of Mathematics, Polish Academy of Sciences","date_created":"2022-12-22T10:08:23Z","status":"public","type":"journal_article","_id":"34835","department":[{"_id":"102"}],"user_id":"93826","intvolume":"       204","page":"165-184","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>","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>.","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} }","short":"J. Klüners, Acta Arithmetica 204 (2022) 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>"},"publication_identifier":{"issn":["0065-1036","1730-6264"]},"publication_status":"published","doi":"10.4064/aa211207-16-5","date_updated":"2023-03-06T08:48:33Z","volume":204,"author":[{"first_name":"Jürgen","id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners"}]},{"publication":"Acta Arithmetica","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."}],"external_id":{"arxiv":["1803.02056 "]},"keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"issue":"3","year":"2020","publisher":"Institute of Mathematics, Polish Academy of Sciences","date_created":"2022-12-22T10:51:13Z","title":"Imaginary quadratic number fields with class groups of small exponent","type":"journal_article","status":"public","_id":"34842","department":[{"_id":"102"}],"user_id":"93826","publication_identifier":{"issn":["0065-1036","1730-6264"]},"publication_status":"published","page":"217-233","intvolume":"       193","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} }","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>.","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>","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>."},"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","id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners"},{"first_name":"Florin","last_name":"Nicolae","full_name":"Nicolae, Florin"}],"doi":"10.4064/aa180220-20-3"},{"status":"public","type":"journal_article","_id":"34892","department":[{"_id":"102"}],"user_id":"93826","intvolume":"       122","page":"185-194","citation":{"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>","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>.","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>.","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>","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>.","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} }","short":"J. Klüners, Acta Arithmetica 122 (2006) 185–194."},"publication_identifier":{"issn":["0065-1036","1730-6264"]},"publication_status":"published","doi":"10.4064/aa122-2-3","date_updated":"2023-03-06T09:52:41Z","volume":122,"author":[{"first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners"}],"abstract":[{"lang":"eng","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). "}],"publication":"Acta Arithmetica","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["math/0411484"]},"year":"2006","issue":"2","title":"The number of S₄-fields with given discriminant","publisher":"Institute of Mathematics, Polish Academy of Sciences","date_created":"2022-12-23T09:40:25Z"}]