4 papers
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…
Connections Between Combinations Without Specified Separations and Strongly Restricted Permutations, Compositions, and Bit Strings
Michael A. Allen
Let and be, respectively, the number of subsets and -subsets of such that no two subset elements differ by an element of the set $\…
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…
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…