Traces of pth Hecke operators and p-adic hypergeometric functions

Abstract: McCarthy defined hypergeometric functions in the p-adic setting using p-adic gamma functions. This function can be described as p-adic analogue of classical hypergeometric function. In this talk we discuss the traces of pth Hecke operators acting on spaces of cusp forms of weight k and level 1 and their relations with p-adic hypergeometric functions. As a consequence of this result we establish relations of Ramanujan’s tau-function and p-adic hypergeometric functions. This is a joint work with Sudhir Pujahari.

number theory

Audience: researchers in the topic

Warsaw Number Theory Seminar