关于具有三个正则奇点的通用微分方程的解(关于kz3的解)

Q4 Mathematics

Confluentes Mathematici Pub Date : 2020-03-09 DOI:10.5802/cml.59

V. H. N. Minh

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引用次数: 4

摘要

本文讨论了一类特殊的Knizhnik-Zamolodchikov方程(KZ3)的解，以及我们最近关于zeta函数在若干变量上的组合方面的结果。特别地，我们描述了KZ3的微分伽罗瓦群对其解的渐近展开式的作用，导致一个包含唯一的Drinfel 'd关联子(或Drinfel 'd级数)的关联子群。在对多指数多对数和调和和的代数结构和奇异性分析的基础上，给出了带有理系数的结合子的非平凡表达式。

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On the solutions of the universal differential equation with three regular singularities (On solutions of KZ 3 )

This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations (KZ3) and our recent results on combinatorial aspects of zeta functions on several variables. In particular, we describe the action of the differential Galois group of KZ3 on the asymptotic expansions of its solutions leading to a group of associators which contains the unique Drinfel’d associator (or Drinfel’d series). Non trivial expressions of an associator with rational coefficients are also explicitly provided, based on the algebraic structure and the singularity analysis of the multi-indexed polylogarithms and harmonic sums.

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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.