Universal ${\mathbb{F}}_q-$Family of $v-$adic Multiple Zeta Values over Function Fields

Abstract

This paper aims to study the ${\mathbb{F}}_q-$linear relations between interpolated $v-$adic multiple zeta values over function fields. We proved a universal family of linear relations of interpolated $v-$adic MZVs, which is conjectured to generate all linear relations over ${\mathbb{F}}_q$. At the end of the paper, we also show that these relations can be generalized to all multiple harmonic type sums.

21pages