Upper bounds for shifted moments of quadratic Dirichlet $L$-functions over function fields

TL;DR

This paper derives precise upper bounds for shifted moments of quadratic Dirichlet L-functions over function fields and applies these results to bound moments of quadratic Dirichlet character sums.

Contribution

It provides the first sharp upper bounds for these shifted moments in the function field setting, advancing understanding of L-functions and character sums.

Findings

Established sharp upper bounds for shifted moments of quadratic Dirichlet L-functions.

Derived bounds for moments of quadratic Dirichlet character sums.

Enhanced the theoretical framework for analyzing L-functions over function fields.

Abstract

We establish sharp upper bounds on shifted moments of quadratic Dirichlet $L$-functions over function fields. As an application, we prove some bounds for moments of quadratic Dirichlet character sums over function fields.