Elliptic curves and Thompson's sporadic simple group
Number Theory
2021-02-24 v2
Abstract
We characterize all infinite-dimensional graded virtual modules for Thompson's sporadic simple group, whose graded traces are weight 3/2 weakly holomorphic modular forms satisfying certain special properties. We then use these modules to detect the non-triviality of Mordell--Weil, Selmer, and Tate--Shafarevich groups of quadratic twists of certain elliptic curves.
Keywords
Cite
@article{arxiv.2008.01607,
title = {Elliptic curves and Thompson's sporadic simple group},
author = {Maryam Khaqan},
journal= {arXiv preprint arXiv:2008.01607},
year = {2021}
}
Comments
31 pages, accepted for publication in Journal of Number Theory