一元扩张与微分方程（Bloch–Vlasenko之后）

IF 1.2 3区数学 Q1 MATHEMATICS

Communications in Number Theory and Physics Pub Date : 2020-08-08 DOI:10.4310/cntp.2022.v16.n4.a5

M. Kerr

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引用次数: 6

摘要

S.Bloch和M.Vlasenko最近引入了一个由Hodge结构的几何变分的Mellin变换周期给出的运动伽玛函数理论，他们将其与变分的某些单势扩展的单调性和渐近性联系起来。在这里，我们进一步研究了这些伽玛函数和VHS的相关\emph｛Apery和Frobenius不变量｝，并建立了与动力上同调和非齐次Picard-Fuchs方程解的关系。

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Unipotent extensions and differential equations (after Bloch–Vlasenko)

S. Bloch and M. Vlasenko recently introduced a theory of \emph{motivic Gamma functions}, given by periods of the Mellin transform of a geometric variation of Hodge structure, which they tie to the monodromy and asymptotic behavior of certain unipotent extensions of the variation. Here we further examine these Gamma functions and the related \emph{Apery and Frobenius invariants} of a VHS, and establish a relationship to motivic cohomology and solutions to inhomogeneous Picard-Fuchs equations.

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来源期刊

Communications in Number Theory and Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Focused on the applications of number theory in the broadest sense to theoretical physics. Offers a forum for communication among researchers in number theory and theoretical physics by publishing primarily research, review, and expository articles regarding the relationship and dynamics between the two fields.