The Dwork-Frobenius operator on hypergeometric series

TL;DR

This paper studies the Dwork-Frobenius operator's effect on specific hypergeometric series, leading to new integrality results for their coefficients and classical hypergeometric series.

Contribution

It introduces a detailed analysis of the Dwork-Frobenius operator on hypergeometric series and establishes integrality properties for their coefficients.

Findings

Proves integrality of coefficients for certain hypergeometric series

Extends integrality results to classical hypergeometric series

Provides a new perspective on the action of Frobenius operators

Abstract

We describe the action of the Dwork-Frobenius operator on certain $A$-hypergeometric series. As a consequence, we obtain an integrality result for the coefficients of those series. This implies an integrality result for classical hypergeometric series.