Rudnick and Soundarajan's Theorem over Prime Polynomials for the Rational Function Field

TL;DR

This paper extends the methods of Andrade, Rudnick, and Soundarajan to establish lower bounds for moments of quadratic Dirichlet L-functions over function fields, specifically focusing on prime polynomial cases.

Contribution

It provides a new proof of lower bounds for moments of quadratic Dirichlet L-functions over rational function fields using advanced analytic techniques.

Findings

Established lower bounds for moments of quadratic Dirichlet L-functions

Applied methods from Andrade, Rudnick, and Soundarajan to prime polynomial cases

Enhanced understanding of L-functions in the context of function fields

Abstract

In this paper, we use the methods of Andrade, Rudnick and Soundarajan to prove a Theorem about Lower bounds of moments of quadratic Dirichlet L-functions associated to monic irreducible polynomials over function fields.