%0 Journal Article
%T Rank statistics for a family of elliptic curves over a function field
%A Carl Pomerance
%A Igor E. Shparlinski
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0903.2866v1