{"volume":122,"external_id":{"arxiv":["math/0411484"]},"publication_status":"published","user_id":"93826","title":"The number of S₄-fields with given discriminant","status":"public","author":[{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"}],"page":"185-194","publisher":"Institute of Mathematics, Polish Academy of Sciences","department":[{"_id":"102"}],"doi":"10.4064/aa122-2-3","keyword":["Algebra and Number Theory"],"issue":"2","type":"journal_article","date_updated":"2023-03-06T09:52:41Z","intvolume":"       122","publication":"Acta Arithmetica","date_created":"2022-12-23T09:40:25Z","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0065-1036","1730-6264"]},"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"}],"citation":{"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>.","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>","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>","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} }"},"year":"2006","_id":"34892"}