Shifted moments of cubic and quartic Dirichlet $L$-functions

TL;DR

This paper derives upper bounds for shifted moments of cubic and quartic Dirichlet L-functions assuming GRH, and applies these bounds to estimate moments of related Dirichlet character sums.

Contribution

It provides the first upper bounds for shifted moments of cubic and quartic Dirichlet L-functions under GRH, advancing understanding of their value distribution.

Findings

Established upper bounds for shifted moments under GRH

Derived bounds for moments of Dirichlet character sums

Enhanced understanding of L-function behavior in cubic and quartic cases

Abstract

We establish upper bounds for shifted moments of cubic and quartic Dirichlet $L$-functions under the generalized Riemann hypothesis. As an application, we prove bounds for moments of cubic and quartic Dirichlet character sums.