Rank statistics for a family of elliptic curves over a function field

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dc.creatorPomerance, Carl
dc.creatorShparlinski, Igor E.
dc.date2009-03-16
dc.date.accessioned2026-07-07T12:53:06Z
dc.date.available2026-07-07T12:53:06Z
dc.descriptionWe show that the average and typical ranks in a certain parametric family of elliptic curves described by D. Ulmer tend to infinity as the parameter $d \to\infty$. This is perhaps unexpected since by a result of A. Brumer, the average rank for all elliptic curves over a function field of positive characteristic is asymptotically bounded above by 2.3.
dc.identifierhttps://arxiv.org/abs/0903.2866
dc.identifierhttp://arxiv.org/abs/0903.2866
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223506
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11N25, 11R37, 14H52
dc.titleRank statistics for a family of elliptic curves over a function field
dc.typetext

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