Rank statistics for a family of elliptic curves over a function field
Number Theory
2009-03-18 v1 Algebraic Geometry
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 . 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.
Cite
@article{arxiv.0903.2866,
title = {Rank statistics for a family of elliptic curves over a function field},
author = {Carl Pomerance and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:0903.2866},
year = {2009}
}