Almost all elliptic curves are Serre curves

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dc.creatorJones, Nathan
dc.date2006-11-03
dc.date.accessioned2026-07-07T07:32:31Z
dc.date.available2026-07-07T07:32:31Z
dc.descriptionUsing a multidimensional large sieve inequality, we obtain a bound for the mean square error in the Chebotarev theorem for division fields of elliptic curves that is as strong as what is implied by the Generalized Riemann Hypothesis. As an application we prove a theorem to the effect that, according to height, almost all elliptic curves are Serre curves, where a Serre curve is an elliptic curve whose torsion subgroup, roughly speaking, has as much Galois symmetry as possible.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/math/0611096
dc.identifierhttp://arxiv.org/abs/math/0611096
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/119139
dc.subjectNumber Theory
dc.subject11G05, 11R45
dc.titleAlmost all elliptic curves are Serre curves
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