On Jacobi Sums, Multinomial Coefficients, and p-adic Hypergeometric Functions

Abstract

We extend the methods of our previous article to express special values of p-adic hypergeometric functions in terms of the p-adic gamma function and Jacobi sums over general finite fields. These results are obtained via p-adic congruences for Jacobi sums in terms of multinomial coefficients, and allow one to more fully exploit classical hypergeometric identities to obtain p-adic unit root formulae.