Frobenius structures on hypergeometric equations

TL;DR

This paper explores Frobenius structures on hypergeometric equations, linking Dwork's construction with Gelfand-Kapranov-Zelevinsky's interpretation, and provides explicit formulas involving p-adic gamma functions.

Contribution

It offers a detailed exposition connecting Frobenius structures with hypergeometric systems and derives explicit degeneration formulas at zero.

Findings

Explicit formulas for degeneration at 0 using p-adic gamma functions

Connection between Dwork's Frobenius structures and A-hypergeometric systems

Enhanced understanding of hypergeometric equations in p-adic context

Abstract

We give an exposition of Dwork's construction of Frobenius structures associated to generalized hypergeometric equations via the interpretation of the latter due to Gelfand-Kapranov-Zelevinsky in the language of A-hypergeometric systems. As a consequence, we extract some explicit formulas for the degeneration at 0 in terms of the Morita p-adic gamma function.