Zero Distribution of $v-$adic Multiple Zeta Values over $\mathbb{F}_q(t)$

Abstract

This paper aims to study the zero distribution of $v-$adic multiple zeta values over function fields. We show that the interpolated $v-$adic MZVs at negative integers only vanish at what we call the ''trivial zeros'', for degree one prime over rational function fields. And we conjecture that this result can be generalized to all primes.