Ling Long

Affiliation: Louisiana State University

Title Of Talk: Atkin and Swinnerton-Dyer Congruences for meromorphic modular forms

URLS:
https://arxiv.org/pdf/2511.05718

Abstract: In the 1970's, Atkin and Swinnerton-Dyer conjectured that Fourier coefficients of holomorphic modular cusp forms on noncongruence subgroups satisfy certain $p$-adic recurrence relations which are analogous to Hecke's recurrence relations for congrunece subgroups. In 1985, this was proven in seminal work of Scholl and it was recently extended to weakly holomorphic modular forms by Kazalicki and Scholl. We show that Atkin and Swinnerton-Dyer type congruences extend to the setting of meromorphic modular forms. This is a joint work with Michael Allen and Hasan Saad.

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