Algebraic independence of arithmetic gamma values and Carlitz zeta values

TL;DR

This paper proves comprehensive algebraic independence results for special values of the arithmetic gamma function at fractions and the Carlitz zeta function at integers over function fields.

Contribution

It provides the first complete algebraic independence results for these values in the context of function fields.

Findings

Complete algebraic independence results established.

Values at fractions and integers are shown to be algebraically independent.

Advances understanding of special function values over function fields.

Abstract

We consider the values at proper fractions of the arithmetic gamma function and the values at positive integers of the zeta function for F_q[theta] and provide complete algebraic independence results for them.