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

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We 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.

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Number Theory, Algebraic Geometry, 11N25, 11R37, 14H52

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http://salesiana.dossiersoluciones.com/handle/123456789/223506

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0903.2866
 http://arxiv.org/abs/0903.2866

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arXiv