Algebraic independence of values of Goss L-functions at s=1

TL;DR

This paper studies the algebraic independence and transcendence of special values of Goss L-functions at s=1 over rings with class number one, providing new results in function field arithmetic.

Contribution

It establishes novel results on the algebraic independence and transcendence of Goss L-function values at s=1, expanding understanding in function field number theory.

Findings

Proved algebraic independence of Goss L-function values at s=1.

Established transcendence results for these special values.

Focused on rings of class number one.

Abstract

We investigate special values of Goss L-functions for Dirichlet characters at s=1 over rings of class number one and prove results on their transcendence and algebraic independence.