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S. Bloch and M. Vlasenko recently introduced a theory of \emph{motivic Gammafunctions}, given by periods of the Mellin transform of a geometric variationof Hodge structure, which they tie to the monodromy and asymptotic behavior ofcertain unipotent extensions of the variation. Here we further examine theseGamma functions and the related \emph{Ap\'ery and Frobenius invariants} of aVHS, and establish a relationship to motivic cohomology and solutions toinhomogeneous Picard-Fuchs equations.

Unipotent extensions and differential equations (after Bloch-Vlasenko)