A quadratic hypergeometric 2F1 transformation over finite fields
Number Theory
2016-07-25 v4
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.
Cite
@article{arxiv.1511.00020,
title = {A quadratic hypergeometric 2F1 transformation over finite fields},
author = {Ron Evans and John Greene},
journal= {arXiv preprint arXiv:1511.00020},
year = {2016}
}
Comments
Replaced Corollary 3 with a stronger result, Theorem 3; updated reference [5]; to appear in Proc. Amer. Math. Soc