On Dwork's p-adic formal congruences theorem and hypergeometric mirror maps

by Delaygue, E., (Eric)

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Title Statements

Full title :On Dwork's p-adic formal congruences theorem and hypergeometric mirror maps / E. Delaygue, T. Rivoal, J. Roques.

Summary

"Using Dwork's theory, we prove a broad generalization of his famous -adic formal congruences theorem. This enables us 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, we provide an explicit formula for the "Eisenstein constant" of any hypergeometric series with rational parameters. As an application of these results, we 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."--Publisher website

Edition Statements

Publication Date:©2016

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, Rhode Island
Language:eng
Publication Date:©2016

Notes

"Volume 246, Number 1163 (second of 6 numbers), March 2017."

The Physical Object

Description:1 online resource (v, 94 pages)

Edition Identifiers

ISBN:9781470436353, 1470436353
oclc:ocn968205459
LC Classification:QA564
Dewey Decimal:512.7/4

Subjects

Analyse p-adique Congruences (Géométrie) Congruences (Geometry) Géométrie algébrique Geometry, Algebraic MATHEMATICS -- Algebra Mirror symmetry p-adic analysis Symétrie du miroir