Values of certain L-series in positive characteristic

TL;DR

This paper introduces a family of L-series in positive characteristic, connecting Dirichlet characters and Carlitz-Goss zeta values, and provides formulas and arithmetic properties for their special values.

Contribution

It develops a unified framework for L-series in positive characteristic and derives new formulas for their values at 1 and other positive integers.

Findings

Formula for L-series values at 1

Arithmetic properties of L-series at positive integers

Connection between Dirichlet characters and Carlitz-Goss zeta values

Abstract

We introduce a family of L-series specialising to both L-series associated to certain Dirichlet characters over F_q[T] and to integral values of Carlitz-Goss zeta function associated to F_q[T]. We prove, with the use of the theory of deformations of vectorial modular forms, a formula for their value at 1, as well as some arithmetic properties of other values at positive integers