6 papers · 1 filter
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…
Hypergeometric Distributions and Joint Families of Elliptic Curves
Brian Grove, Hasan Saad
Recently, the first author as well as the second author with Ono, Pujahari, and Saikia determined the limiting distribution of values of certain finite field and ${_3F_2}…
On Some Hypergeometric Modularity Conjectures of Dawsey and McCarthy
Brian Grove
In recent work, the author, in collaboration with Allen, Long, and Tu, developed the Explicit Hypergeometric Modularity Method (EHMM), which establishes the modularity of a large c…
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…
Hypergeometric Moments and Hecke Trace Formulas
Brian Grove
Moments for hypergeometric functions over finite fields were studied in the work of Ono, Pujahari, Saad, and Saikia for several and cases. We generalize the…