Hypergeometric motives from Euler integral representations

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.