Multizeta values for F_q[t], their period interpretation and relations between them

TL;DR

This paper interprets multizeta values over function fields through iterated extensions of Carlitz motives, revealing complex relations and providing a deeper understanding of their structure.

Contribution

It introduces a period interpretation of multizeta values in the function field setting using explicit iterated extensions of Carlitz motives.

Findings

Explicit relations among multizeta values are demonstrated.

A new period interpretation connects multizeta values to t-motives.

Examples of combinatorial relations are provided.

Abstract

We provide a period interpretation for multizeta values (in the function field context) in terms of explicit iterated extensions of tensor powers of Carlitz motives (mixed Carlitz-Tate t-motives). We give examples of combinatorially involved relations that these multizeta values satisfy.