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arXiv · 0903.2866

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

Carl Pomerance·Igor E. Shparlinski
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Abstract

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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Carl Pomerance, Igor E. Shparlinski. 2009-03-16. Rank statistics for a family of elliptic curves over a function field. https://arxiv.org/abs/0903.2866

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