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On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps (Memoirs of the American Mathematical Society)

Mathematical Theory

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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.

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Format: paperback
ASIN: 1470423006
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Theory
Domain: Amazon UK
Release Date: 30 March 2017
Listed Since: 21 December 2016

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On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps (Memoirs of the American Mathematical Society)

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