Appell series over finite fields and gaussian hypergeometric series

Abstract

In this thesis we study classical hypergeometric series and Appell series over finite fields and find finite field analogues of several product and summation formulas satisfied by the classical hypergeometric series Hypergeometric functions over finite fields are known as Gaussian hypergeometric series As an application of the product and summation formulas we deduce several special vlaues of 2F1 3F2 and 4F3 Gaussian hypergeometric series Some of our special values of Gaussian hypergeometr...