Abstract
Abstract
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.
Publisher
Canadian Mathematical Society