Multiple zeta values over global function fields

TL;DR

This paper develops the analytic theory of a multiple zeta function over global function fields, extending the classical Euler-Zagier multiple zeta function to the function field setting.

Contribution

It introduces a new multiple zeta function over global function fields and establishes its analytic properties, providing a foundational framework for future research.

Findings

Defined the multiple zeta function over global function fields

Established basic analytic properties of the function

Extended classical multiple zeta theory to the function field context

Abstract

In this paper we develop the analytic theory of a multiple zeta function in d independent complex variables defined over a global function field. This is the function field analog of the Euler-Zagier multiple zeta function of depth d.