Moments of Dirichlet $L$-functions to a fixed modulus over function fields

TL;DR

This paper determines the typical size of the moments of Dirichlet L-functions at the center for a fixed prime modulus over function fields, covering all real moments.

Contribution

It establishes the expected order of magnitude for the moments of Dirichlet L-functions over function fields for all real k, extending previous results.

Findings

Expected order of magnitude for moments of Dirichlet L-functions

Results valid for all real k ≥ 0

Advances understanding of L-function behavior in function fields

Abstract

In this paper, we establish the expected order of magnitude of the $k$th-moment of central values of the family of Dirichlet $L$-functions to a fixed prime modulus over function fields for all real $k \geq 0$.