Unipotent extensions and differential equations (after Bloch-Vlasenko)

S. Bloch and M. Vlasenko recently introduced a theory of motivic Gamma functions, given by periods of the Mellin transform of a geometric variation of Hodge structure. They tie properties of these functions to the monodromy and asymptotic behavior of certain unipotent extensions of the variation. In this article, we further examine their Gamma functions and the related Apéry and Frobenius invariants of a VHS, and establish a relationship to motivic cohomology and solutions to inhomogeneous Picard-Fuchs equations.