论文标题
在$ \ mathbb {f} _q [t] $上消失多个zeta值
Vanishing of Multiple Zeta Values over $\mathbb{F}_q[t]$ at Negative Integers
论文作者
论文摘要
令$ \ mathbb {f} _q $为$ q $元素的有限字段。在本文中，我们研究了$ \ mathbb {f} _q [t] $在负整数上的多Zeta值的消失行为。这些值是经典多Zeta值的类似物。在负整数中，它们是一系列功率总和$ s_d（k）$的产品，这些产品是$ t $的多项式。通过研究$ s_d（s）$的$ t $价值（$ s <0 $），我们表明，负整数的Multizeta值仅在Trivial Zeros中消失。证据的灵感来自于卡里茨（Carlitz）的“贪婪元素”陈述的证据。
Let $\mathbb{F}_q$ be the finite field of $q$ elements. In this paper, we study the vanishing behavior of multizeta values over $\mathbb{F}_q[t]$ at negative integers. These values are analogs of the classical multizeta values. At negative integers, they are series of products of power sums $S_d(k)$ which are polynomials in $t$. By studying the $t$-valuation of $S_d(s)$ for $s < 0$, we show that multizeta values at negative integers vanish only at trivial zeros. The proof is inspired by the idea of Sheats in the proof of a statement of "greedy element" by Carlitz.
