Elliptic curves and Thompson?s sporadic simple group

JOURNAL OF NUMBER THEORY

卷:224

Article

Khaqan, Maryam¹ 

[1] Emory Univ, Dept Math, 400 Dowman Dr, Atlanta, GA 30322 USA

关键词: Moonshine;    Number theory;    Sporadic groups;    Finite groups;    Discrete groups;    Modular forms;    Harmonic Maa? forms;    Birch and Swinnerton-Dyer;    Conjecture;    L-function;    Elliptic curves;    Selmer group;    Mock modular forms;    Rademacher sums;    Quadratic forms;    Traces of singular moduli;   

DOI  :  10.1016/j.jnt.2021.01.015

来源: Elsevier

【 摘 要 】

We characterize all infinite-dimensional graded virtual modules for Thompson's sporadic simple group whose graded traces are weight 32 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. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free