We define a hypergeometric function over finite fields which is an analogue of the classical generalized hypergeometric series. We prove that this function satisfies many transformation and summation formulas. Some of these results are analogous to those given by Dixon, Kummer and Whipple for the well-poised classical series. We also discuss this functions relationship to other finite field analogues of the classical series, most notably those defined by Greene and Katz.
- Character sums
- Gauss sums
- Hypergeometric function over finite fields
- Modular forms
- Transformations of hypergeometric series