What question did this study set out to answer?

The aim is to explore the relationship between hypergeometric functions and their associated zeta functions using Euler's integral representations.

February 8, 2026Open Access

Hypergeometric motives from Euler integral representations

Key Points

The aim is to explore the relationship between hypergeometric functions and their associated zeta functions using Euler's integral representations.
Revisiting one-parameter families of affine covers based on Euler's integrals.
Introducing a partial compactification of these families.
Developing a combinatorial algorithm for Hodge number computation.
Zeta functions of the fibers expressible as products of series linked to hypergeometric motives.
Connection to zeta functions of tori affirmed, with the influence of Hecke grössencharacters.

Abstract

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 ‐series attached to nondegenerate hypergeometric motives and zeta functions of tori, twisted by Hecke Grössencharacters. This permits a combinatorial algorithm for computing the Hodge numbers of the family.

Hypergeometric motives from Euler integral representations

Key Points

Abstract

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