Hybrid Euler-Hadamard product for quadratic Dirichlet $L$-functions in function fields

TL;DR

This paper introduces a hybrid Euler-Hadamard product model for quadratic Dirichlet L-functions over function fields, computes initial moments, and supports conjectural asymptotic formulas for these moments.

Contribution

It develops a novel hybrid model for quadratic Dirichlet L-functions in function fields and computes initial moments to support conjectures.

Findings

Computed the first three twisted moments of the L-functions.

Provided evidence supporting conjectural asymptotic formulas.

Extended the hybrid model approach to function fields.

Abstract

We develop a hybrid Euler-Hadamard product model for quadratic Dirichlet $L$--functions over function fields (following the model introduced by Gonek, Hughes and Keating for the Riemann-zeta function). After computing the first three twisted moments in this family of $L$--functions, we provide further evidence for the conjectural asymptotic formulas for the moments of the family.