正特征下多个zeta值的代数结构

IF 1.8 2区 数学 Q1 MATHEMATICS
Chieh-Yu Chang, Yen-Tsung Chen, Yoshinori Mishiba
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引用次数: 4

摘要

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。
Algebra structure of multiple zeta values in positive characteristic
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.
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CiteScore
3.10
自引率
0.00%
发文量
7
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