The number of S₄-fields with given discriminant
J. Klüners, Acta Arithmetica 122 (2006) 185–194.
Download
No fulltext has been uploaded.
Journal Article
| Published
| English
Author
Department
Abstract
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).
Keywords
Publishing Year
Journal Title
Acta Arithmetica
Volume
122
Issue
2
Page
185-194
LibreCat-ID
Cite this
Klüners J. The number of S₄-fields with given discriminant. Acta Arithmetica. 2006;122(2):185-194. doi:10.4064/aa122-2-3
Klüners, J. (2006). The number of S₄-fields with given discriminant. Acta Arithmetica, 122(2), 185–194. https://doi.org/10.4064/aa122-2-3
@article{Klüners_2006, title={The number of S₄-fields with given discriminant}, volume={122}, DOI={10.4064/aa122-2-3}, number={2}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish Academy of Sciences}, author={Klüners, Jürgen}, year={2006}, pages={185–194} }
Klüners, Jürgen. “The Number of S₄-Fields with given Discriminant.” Acta Arithmetica 122, no. 2 (2006): 185–94. https://doi.org/10.4064/aa122-2-3.
J. Klüners, “The number of S₄-fields with given discriminant,” Acta Arithmetica, vol. 122, no. 2, pp. 185–194, 2006, doi: 10.4064/aa122-2-3.
Klüners, Jürgen. “The Number of S₄-Fields with given Discriminant.” Acta Arithmetica, vol. 122, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2006, pp. 185–94, doi:10.4064/aa122-2-3.
arXiv 
Google Scholar