Frobenius map and the p-adic Gamma function

2010/06/02 by Ilya Shapiro, Shapiro, Ilya
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1006.0382

8 pages

arxiv created 2010/06/02 · arxiv updated 2010/06/03

Abstract

In this note we study the relationship between the power series expansion of the Dwork exponential and the Mahler expansion of the p-adic Gamma function. We exploit this relationship to prove that certain quantities that appeared in our previous computations of the Frobenius map can be expressed in terms of the derivatives of the p-adic Gamma function at 0. This is used to prove a conjecture about the non-trivial off-diagonal entry in the Frobenius matrix of the mirror quintic threefold.

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