A quadratic hypergeometric 2F1 transformation over finite fields

Abstract

In 1984, the second author conjectured a quadratic transformation formula which relates two hypergeometric 2F1 functions over a finite field F_q. We prove this conjecture and give an application. The proof depends on a new linear transformation formula for pseudo hypergeometric functions over F_q.

Replaced Corollary 3 with a stronger result, Theorem 3; updated reference [5]; to appear in Proc. Amer. Math. Soc