Rudnick and Soundararajan's Theorem for Function Fields

TL;DR

This paper proves a function field analogue of Rudnick and Soundararajan's theorem, establishing lower bounds for moments of quadratic Dirichlet L-functions over hyperelliptic curves in the large genus limit.

Contribution

It introduces a new lower bound result for moments of quadratic Dirichlet L-functions in the function field setting, extending prior number field results.

Findings

Lower bounds for moments of quadratic Dirichlet L-functions over hyperelliptic curves.

Results valid in the large genus limit.

Extension of Rudnick and Soundararajan's theorem to function fields.

Abstract

In this paper we prove a function field version of a theorem by Rudnick and Soundararajan about lower bounds for moments of quadratic Dirichlet $L$-functions. We establish lower bounds for the moments of quadratic Dirichlet $L$--functions associated to hyperelliptic curves of genus $g$ over a fixed finite field $\mathbb{F}_{q}$ in the large genus $g$ limit.