Hypergeometric Motives from Euler Integral Representations

Fuente: arXiv
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Main Authors: Kelly, Tyler L., Voight, John
Format: Preprint
Published: 2024
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author Kelly, Tyler L.
Voight, John
author_facet Kelly, Tyler L.
Voight, John
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2412_03257
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Hypergeometric Motives from Euler Integral Representations
Kelly, Tyler L.
Voight, John
Number Theory
11G40, 11S40, 11T24, 14C15, 14G10, 33C20
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.
title Hypergeometric Motives from Euler Integral Representations
topic Number Theory
11G40, 11S40, 11T24, 14C15, 14G10, 33C20
url https://arxiv.org/abs/2412.03257