Arithmetic Constraints on Hypergeometric Identities

Abstract

The standard literature on special functions contains a lot of hypergeometric identities involving products and quotients of gamma functions, but still the occurrence of such identities is a sporadic phenomenon. This is because the existence of them is constrained by severe arithmetic conditions. We demonstrate this kind of constraints by focusing on a certain data region where the essential nature of the issue comes out clearly.

24 pages, 1 figure