Dwork's congruences for the constant terms of powers of a Laurent polynomial

TL;DR

This paper proves that the constant terms of Laurent polynomial powers follow specific prime power congruences, leading to p-adic analytic continuation properties akin to Dwork's hypergeometric series results.

Contribution

It establishes new congruences for Laurent polynomial constant terms and connects these to p-adic analytic continuation, extending Dwork's hypergeometric series work.

Findings

Constant terms satisfy prime power congruences

Generated series admits p-adic analytic continuation

Extends Dwork's hypergeometric series results

Abstract

We prove that the constant terms of powers of a Laurent polynomial satisfy certain congruences modulo prime powers. As a corollary, the generating series of these numbers considered as a function of a p-adic variable satisfies a non-trivial analytic continuation property, similar to what B. Dwork showed for a class of hypergeometric series.