Moments of quadratic Dirichlet $L$-functions over Function Fields

TL;DR

This paper determines the expected size of the moments of quadratic Dirichlet L-functions over function fields, providing insights into their behavior for various moments and prime moduli.

Contribution

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

Findings

Expected order of magnitude for the moments of L-functions

Results valid for all real moments $k \\geq 0$

Applicable to hyperelliptic curves and prime moduli

Abstract

In this paper, we establish the expected order of magnitude of the $k$th-moment of quadratic Dirichlet $L$-functions associated to hyperelliptic curves of genus $g$ as well as of prime moduli over a fixed finite field $\mathbb{F}_{q}$ for all real $k \geq 0$.