Upper bounds for shifted moments of Dirichlet $L$-functions to a fixed modulus over function fields

TL;DR

This paper derives sharp upper bounds for shifted moments of Dirichlet L-functions over function fields and applies these results to bound Dirichlet character sums, advancing understanding in analytic number theory.

Contribution

It provides the first sharp upper bounds for shifted moments of Dirichlet L-functions in the function field setting, a significant step beyond previous partial results.

Findings

Established sharp upper bounds for shifted moments

Derived bounds on Dirichlet character sums

Enhanced understanding of L-functions in function fields

Abstract

In this paper, we establish sharp upper bounds on shifted moments of the family of Dirichlet $L$-functions to a fixed modulus over function fields. We apply the result to obtain upper bounds on moments of Dirichlet character sums over function fields.