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

2013/06/24 by Anton Mellit, Mellit, Anton, Masha Vlasenko +1 · 2 citations
Computer Science · Mathematics · #11G25 #11Sxx #14G10 #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1306.5811

openalex publication_date 2013/06/24 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

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

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