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arXiv · 1612.09249

Zeta functions of alternate mirror Calabi-Yau families

Charles F. Doran·Tyler L. Kelly·Adriana Salerno·Steven Sperber·John Voight·Ursula Whitcher
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Abstract

We prove that if two Calabi-Yau invertible pencils have the same dual weights, then they share a common factor in their zeta functions. By using Dwork cohomology, we demonstrate that this common factor is related to a hypergeometric Picard--Fuchs differential equation. The factor in the zeta function is defined over the rationals and has degree at least the order of the Picard--Fuchs equation. As an application, we relate several pencils of K3 surfaces to the Dwork pencil, obtaining new cases of arithmetic mirror symmetry.

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Charles F. Doran, Tyler L. Kelly, Adriana Salerno, Steven Sperber, John Voight, Ursula Whitcher. 2016-12-29. Zeta functions of alternate mirror Calabi-Yau families. https://arxiv.org/abs/1612.09249

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