3 papers
math.NT2025
Atkin and Swinnerton-Dyer congruences for meromorphic modular forms
Michael Allen, Ling Long, Hasan Saad
In the 1970's, Atkin and Swinnerton-Dyer conjectured that Fourier coefficients of holomorphic modular cusp forms on noncongruence subgroups of satisfy cer…
math.NT2024
The Explicit Hypergeometric-Modularity Method II
Michael Allen, Brian Grove, Ling Long +1
In the first paper of this sequence, we provided an explicit hypergeometric modularity method by combining different techniques from the classical, -adic, and finite field setti…
math.NT2024
Holomorphic projection for sesquiharmonic Maass forms
Michael Allen, Olivia Beckwith, Vaishavi Sharma
We study the holomorphic projection of mixed mock modular forms involving sesquiharmonic Maass forms. As a special case, we numerically express the holomorphic projection of a func…