Frobenius map and the $p$-adic Gamma function

Details Frobenius map and the $p$-adic Gamma function Frobenius map and the $p$-adic Gamma function

2010-06-02

arxiv.org/abs/1006.0382v1

Mathematics

Number Theory

8 pages

Scientific paper

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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