The number of $S_4$ fields with given discriminant
| dc.creator | Klueners, Juergen | |
| dc.date | 2004-11-22 | |
| dc.date | 2005-07-27 | |
| dc.date.accessioned | 2026-07-07T05:14:34Z | |
| dc.date.available | 2026-07-07T05:14:34Z | |
| dc.description | We prove that the number of quartic $S_4$--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 $p^2$ is bounded above by $O(p^{1/2}\log(p)^2)$. | |
| dc.description | new version | |
| dc.identifier | https://arxiv.org/abs/math/0411484 | |
| dc.identifier | http://arxiv.org/abs/math/0411484 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73322 | |
| dc.subject | Number Theory | |
| dc.subject | 11R29;11R16, 11R32 | |
| dc.title | The number of $S_4$ fields with given discriminant | |
| dc.type | text |