Dwork's congruences for the constant terms of powers of a Laurent polynomial (1306.5811v1)

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.