Zeta-like Multizeta Values for $\mathbb{F}_q[t]$

TL;DR

This paper investigates relations between multizeta values over function fields, focusing on zeta-like values whose ratios with zeta values are rational, and provides conjectures and data, especially for q=2 and even weights.

Contribution

It establishes proven and conjectural relations among multizeta values over $F_q[t]$, especially characterizing zeta-like values for specific q and weights.

Findings

Descriptions of zeta-like values for q=2 and even weights

Conjectural full classification of zeta-like values in these cases

Supporting data for the proposed conjectures

Abstract

We prove and conjecture several relations between multizeta values for $\mathbb{F}_q[t]$, focusing on zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or equivalently algebraic). In particular, we describe them conjecturally fully for $q=2$, or more generally for any $q$ for `even' weight (`eulerian' tuples). We provide some data in support of the guesses.