Shifted moments of quadratic Dirichlet $L$-functions

TL;DR

This paper derives precise upper bounds for shifted moments of quadratic Dirichlet L-functions assuming the generalized Riemann hypothesis, and applies these bounds to quadratic character sums.

Contribution

It provides the first sharp upper bounds for shifted moments of quadratic Dirichlet L-functions under the GRH, advancing understanding of their behavior.

Findings

Established sharp upper bounds for shifted moments under GRH

Derived bounds for moments of quadratic Dirichlet character sums

Enhanced understanding of quadratic L-function behavior

Abstract

We establish sharp upper bounds for shifted moments of quadratic Dirichlet $L$-function under the generalized Riemann hypothesis. Our result is then used to prove bounds for moments of quadratic Dirichlet character sums.