On Dwork's P-adic Formal Congruences Theorem and Hypergeometric Mirror Maps

Ebook Details


E. Delaygue, T. Rivoal, J. Roques

Year 2017
Pages 94
Publisher Amer Mathematical Society
Language en
ISBN 9781470423001
File Size 749.39 KB
File Format PDF
Download Counter 101
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Ebook Description

Using Dwork's theory, the authors prove a broad generalization of his famous p-adic formal congruences theorem. This enables them to prove certain p-adic congruences for the generalized hypergeometric series with rational parameters* in particular, they hold for any prime number p and not only for almost all primes. Furthermore, using Christol's functions, the authors provide an explicit formula for the "Eisenstein constant" of any hypergeometric series with rational parameters. As an application of these results, the authors obtain an arithmetic statement "on average" of a new type concerning the integrality of Taylor coefficients of the associated mirror maps. It contains all the similar univariate integrality results in the literature, with the exception of certain refinements that hold only in very particular cases.