Multiple zeta values with varying constant fields

TL;DR

This paper investigates multiple zeta values in function fields with different constant fields, proving that no algebraic relations exist between values with different constants using Papanikolas' theory.

Contribution

It demonstrates the independence of multiple zeta values across varying constant fields through the application of $t$-motivic Galois group theory.

Findings

No algebraic relations between multiple zeta values with different constant fields.

Application of Papanikolas' theory to positive characteristic function fields.

Establishment of independence results in the context of varying constant fields.

Abstract

Multiple zeta values associated with function fields with varying constant fields are dealt with simultaneously. Thakur introduced multiple zeta values in the arithmetic of positive characteristic function fields, and the definition depends on the field of constants of the chosen function field. Using Papanikolas' theory on the relationship between the $t$-motivic Galois group and the periods of a pre-$t$-motive, we show that there exist no algebraic relations which relate multiple zeta values with different constants field.