AAG: Hypergeometric Type Modular Forms

Abstract: Using the framework relating hypergeometric motives to modular forms, we can study the arithmetic properties of certain types of modular forms via the hypergeometric arithmetic.  In recent joint projects with Michael Allen, Brian Grove, and Ling Long, we develop and explore an explicit “Hypergeometric-Modularity” method for associating a modular form to a given hypergeometric datum. In particular, for certain hypergeometric data, we confirm the modularity of the corresponding hypergeometric Galois representations by explicit construction of Hecke eigenforms.  

In this talk, I will discuss some special families of such "hypergeometric modular forms", including explicit connections between Beta integral/hypergeometric values and special -values of these -quotients as well as identities among the corresponding hypergeometric values.

Host: Wanlin Li