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.

中文翻译：

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单能扩展和微分方程（根据 Bloch–Vlasenko）

S. Bloch 和 M. Vlasenko 最近介绍了一种动机 Gamma 函数理论，该理论由 Hodge 结构的几何变化的梅林变换周期给出。他们将这些函数的属性与变异的某些单能扩展的单调和渐近行为联系起来。在本文中，我们进一步研究了它们的 Gamma 函数以及 VHS 的相关Apéry 和 Frobenius 不变量，并建立了与动机上同调的关系以及非齐次 Picard-Fuchs 方程的解。