On the typical rank of elliptic curves over ${\mathbb Q}(T)$
Number Theory
2022-03-30 v2
Abstract
We give upper bounds for the number of rational elliptic surfaces in some families having positive rank, obtaining in particular that these form a subset of density zero. This confirms Cowan's conjecture (arXiv:2009.08622v2) in the case .
Keywords
Cite
@article{arxiv.2109.00745,
title = {On the typical rank of elliptic curves over ${\mathbb Q}(T)$},
author = {Francesco Battistoni and Sandro Bettin and Christophe Delaunay},
journal= {arXiv preprint arXiv:2109.00745},
year = {2022}
}