Gaussian hypergeometric functions and supercongruences

Speaker: Robert Osburn

Time: 4:00PM
Date: Wed 27th September 2006

Location: Mathematical Sciences Seminar Room

In 1984, Greene introduced the notion of hypergeometric functions over finite fields. Special values of these functions have recently been of interest as they are related to numbers of F_p points on algebraic varieties and to Fourier coefficients of modular forms. In this talk, we discuss a general modulo p^3 congruence for these functions which yields extensions to recent supercongruences of Ono-Ahlgren, Loh-Rhodes, and of Mortenson. This is joint work with Carsten Schneider (Linz).

(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)