6 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…
Special -values of certain CM weight three Hecke eigenforms
Paresh Arora, Koustav Mondal, Akio Nakagawa +1
Ramanujan's theory of elliptic functions to alternative bases connects modular forms with hypergeometric series and has led to applications such as the modularity of certain hyperg…
Jacquet-Langlands correspondence for non-Eichler orders
Fang-Ting Tu, Yifan Yang
In this note, we give a concrete realization of the Jacquet-Langlands correspondence for non-Eichler orders of indefinite quaternion algebras defined over . To be more p…
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…
Supercongruences arising from Ramanujan-Sato Series
Angelica Babei, Manami Roy, Holly Swisher +2
Recently, the authors with Lea Beneish established a recipe for constructing Ramanujan-Sato series for , and used this to construct 11 explicit examples of Ramanujan-Sato ser…
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…