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

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

2009-03-16

arxiv.org/abs/0903.2866v1

Mathematics

Number Theory

Scientific paper

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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