Zero distribution of v-adic multiple zeta values over 𝔽q(t)

Abstract

This paper aims to study the zero distribution of [Formula: see text]-adic multiple zeta values over function fields. We show that the interpolated [Formula: see text]-adic MZVs at negative integers only vanish at what we call the “trivial zeros”, for degree one finite place over rational function fields. And we conjecture that this result can be generalized to all finite places.