Conditionally bounding analytic ranks of elliptic curves
Number Theory
2011-12-08 v1
Abstract
We describe a method for bounding the rank of an elliptic curve under the assumptions of the Birch and Swinnerton-Dyer conjecture and the generalized Riemann hypothesis. As an example, we compute, under these conjectures, exact upper bounds for curves which are known to have rank at least as large as 20, 21, 22, 23, and 24. For the known curve of rank at least 28, we get a bound of 30.
Keywords
Cite
@article{arxiv.1112.1503,
title = {Conditionally bounding analytic ranks of elliptic curves},
author = {Jonathan W. Bober},
journal= {arXiv preprint arXiv:1112.1503},
year = {2011}
}
Comments
9 pages