论文标题
阳性特征中多个Zeta值的代数结构
Algebra structure of multiple zeta values in positive characteristic
论文作者
论文摘要
本文是[CM20]在阳性特征中功能场上的多个Zeta值（MZV）的研究中的高潮。对于有限字段的任何有限位置$ v $ v $ $ k $，我们证明$ v $ -ADIC MZV可以满足相同的$ \ bar {k} $ - 代数关系，即它们相应的$ \ infty $ \ infty $ - infty $ addic-adic mzv的满意。同等地，我们表明，$ v $ -ADIC MZV的形式形成了一个代数，该代数由$ q $ shuffle产品给出，该产品来自$ \ infty $ -ADIC MZV，并且有一个定义明确的$ \ bar {k} $ - 代数 - 代数 - 来自$ \ infty $ $ $ $ -AdiC $ -AdicmAdiC $ -AdiC $ v- $ -AdicmAdiC $ -AdicmAdiC $ -AdicmAdik-aDik $ v。
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.
