Two term relations between multizeta of depth two for $\mathbb{F}_q[t]$

TL;DR

This paper investigates relations between depth-two multizeta values over function fields, proving new rational relations and additional identities in characteristic 2, advancing understanding of their algebraic structure.

Contribution

It establishes rational relations between depth-two multizeta values and uncovers new identities specifically in characteristic 2.

Findings

Rational relations between multizeta values of depth two and same weight.

Additional relations in characteristic 2.

Enhanced understanding of multizeta value algebra over function fields.

Abstract

We focus on multizeta values of depth two for $\mathbb{F}_q[t]$, where the ratio with another multizeta value of depth two is rational. In characteristic 2, we prove some extra relations between multizeta values of depth 2 and the same weight.