English

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 pp-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}
}