5 papers
The Explicit Hypergeometric Modularity Method III
Brian Grove, Ling Long, Esme Rosen +1
We refine the Explicit Hypergeometric Modularity Method (EHMM) and develop a variant that applies to a broader class of hypergeometric data. As an application, we establish the mod…
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…
The Explicit Hypergeometric-Modularity Method I
Michael Allen, Brian Grove, Ling Long +1
The theories of hypergeometric functions and modular forms are highly intertwined. For example, particular values of truncated hypergeometric functions and hypergeometric character…
Traces of Hecke Operators via Hypergeometric Character Sums
Jerome W. Hoffman, Wen-Ching Winnie Li, Ling Long +1
In this paper we obtain explicit formulas for the traces of Hecke operators on spaces of cusp forms in certain instances related to arithmetic triangle groups. These expressions ar…
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…