Vanishing of Multiple Zeta Values over \mathbbF_q[t] at Negative Integers

2020/03/27 by Shuhui Shi, Shi, Shuhui
Computer Science · Mathematics · #11M32 #11M38 #11R58 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2003.12242

openalex publication_date 2020/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathbbF_q be the finite field of q elements. In this paper, we study the vanishing behavior of multizeta values over \mathbbF_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.

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