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arXiv · 2001.07280

$A$-hypergeometric series and a $p$-adic refinement of the Hasse-Witt matrix

Alan Adolphson·Steven Sperber
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Abstract

We identify the $p$-adic unit roots of the zeta function of a projective hypersurface over a finite field of characteristic $p$ as the eigenvalues of a product of special values of a certain matrix of $p$-adic series. That matrix is a product $F(\Lambda^p)^{-1}F(\Lambda)$, where the entries in the matrix $F(\Lambda)$ are $A$-hypergeometric series with integral coefficients and $F(\Lambda)$ is independent of $p$.

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Alan Adolphson, Steven Sperber. 2020-01-20. $A$-hypergeometric series and a $p$-adic refinement of the Hasse-Witt matrix. https://arxiv.org/abs/2001.07280

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