Event Type:

Number Theory Seminar

Date/Time:

Tuesday, October 7, 2014 - 16:00 to 17:00

Location:

Kidder 236

Local Speaker:

Abstract:

In 1997, van Hamme developed p-adic analogs, of several series which relate hypergeometric series to values of the gamma function, originally studied by Ramanujan. These analogs relate truncated sums of hypergeometric series to values of the p-adic gamma function, and are called Ramanujan type supercongruences. In all, van Hamme conjectured 13 such formulas, three of which were proved by van Hamme himself, and a handful of others have been proved recently using a wide range of methods. We will discuss a method we use to prove most of the remaining supercongruences, revisit some of the proved ones, and provide some extensions as well as more general conjectures.