Atkin and Swinnerton-Dyer congruences and noncongruence modular forms
Number Theory
2014-09-29 v3
Abstract
Atkin and Swinnerton-Dyer congruences are special congruence recursions satisfied by coefficients of noncongruence modular forms. These are in some sense -adic analogues of Hecke recursion satisfied by classic Hecke eigenforms. They actually appeared in different context and sometimes can be obtained using the theory of formal groups. In this survey paper, we introduce the Atkin and Swinnerton-Dyer congruences, and discuss some recent progress on this topic.
Keywords
Cite
@article{arxiv.1303.6228,
title = {Atkin and Swinnerton-Dyer congruences and noncongruence modular forms},
author = {Wen-Ching Winnie Li and Ling Long},
journal= {arXiv preprint arXiv:1303.6228},
year = {2014}
}