A positive proportion of elliptic curves over $\mathbb{Q}$ have rank one
Number Theory
2014-01-03 v1
Abstract
We prove that, when all elliptic curves over are ordered by naive height, a positive proportion have both algebraic and analytic rank one. It follows that the average rank and the average analytic rank of elliptic curves are both strictly positive.
Cite
@article{arxiv.1401.0233,
title = {A positive proportion of elliptic curves over $\mathbb{Q}$ have rank one},
author = {Manjul Bhargava and Christopher Skinner},
journal= {arXiv preprint arXiv:1401.0233},
year = {2014}
}
Comments
19 pages