Algebra structure of multiple zeta values in positive characteristic

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-07-16 DOI:10.4310/cjm.2022.v10.n4.a1

Chieh-Yu Chang, Yen-Tsung Chen, Yoshinori Mishiba

引用次数: 4

Abstract

This paper is a culmination of [CM20] on the study of multiple zeta values (MZV's) over function fields in positive characteristic. For any finite place $v$ of the rational function field $k$ over a finite field, we prove that the $v$-adic MZV's satisfy the same $\bar{k}$-algebraic relations that their corresponding $\infty$-adic MZV's satisfy. Equivalently, we show that the $v$-adic MZV's form an algebra with multiplication law given by the $q$-shuffle product which comes from the $\infty$-adic MZV's, and there is a well-defined $\bar{k}$-algebra homomorphism from the $\infty$-adic MZV's to the $v$-adic MZV's.

查看原文本刊更多论文

正特征下多个zeta值的代数结构

本文是[CM20]对正特征函数场上的多重zeta值(MZV's)的研究的高潮。对于有限域上有理函数域$k$的任意有限位置$v$，我们证明了$v$ -adic MZV与其对应的$\infty$ -adic MZV满足相同的$\bar{k}$ -代数关系。同样地，我们证明了$v$ -adic MZV与来自$\infty$ -adic MZV的$q$ -shuffle积所给出的乘法定律形成了一个代数，并且证明了$\infty$ -adic MZV与$v$ -adic MZV之间存在一个定义良好的$\bar{k}$ -代数同态。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.