Hypergeometric Motives from Euler Integral Representations

Tyler L. Kelly; John Voight

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arXiv · 2412.03257

Hypergeometric Motives from Euler Integral Representations

Tyler L. Kelly·John Voight

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Abstract

We revisit certain one-parameter families of affine covers arising naturally from Euler's integral representation of hypergeometric functions. We introduce a partial compactification of this family. We show that the zeta function of the fibers in the family can be written as an explicit product of $L$-series attached to nondegenerate hypergeometric motives and zeta functions of tori, twisted by Hecke Grossencharacters. This permits a combinatorial algorithm for computing the Hodge numbers of the family.

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Tyler L. Kelly, John Voight. 2024-12-04. Hypergeometric Motives from Euler Integral Representations. https://arxiv.org/abs/2412.03257

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