p-adic hypergeometric series and supercongruences

Speaker: Dermot McCarthy (UCD)

Time: 3:00PM

Date: Wed 28th October 2009

Location: Mathematical Sciences Seminar Room

We discuss recent work in which we generalise Greene's hypergeometric series over finite fields in the p-adic setting. We provide congruences between these p-adic hypergeometric series and truncated ordinary hypergeometric series. We also relate a special value of the p-adic hypergeometric series to the p-th Fourier coefficient of a modular form, thus resolving an outstanding supercongruence conjecture of Rodriguez-Villegas.

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