The number of $S_4$ fields with given discriminant

dc.creatorKlueners, Juergen
dc.date2004-11-22
dc.date2005-07-27
dc.date.accessioned2026-07-07T05:14:34Z
dc.date.available2026-07-07T05:14:34Z
dc.descriptionWe 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.descriptionnew version
dc.identifierhttps://arxiv.org/abs/math/0411484
dc.identifierhttp://arxiv.org/abs/math/0411484
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73322
dc.subjectNumber Theory
dc.subject11R29;11R16, 11R32
dc.titleThe number of $S_4$ fields with given discriminant
dc.typetext

Files

Collections