Lower bounds for shifted moments of Dirichlet $L$-functions of fixed modulus

TL;DR

This paper establishes precise lower bounds for shifted moments of Dirichlet L-functions with fixed modulus, assuming the generalized Riemann hypothesis, advancing understanding of their value distribution.

Contribution

It provides the first sharp lower bounds for shifted moments of Dirichlet L-functions of fixed modulus under GRH.

Findings

Sharp lower bounds for shifted moments are proven.

Results depend on the generalized Riemann hypothesis.

The bounds improve previous estimates in the literature.

Abstract

We establish sharp lower bounds for shifted (with two shifts) moments of Dirichlet $L$-function of fixed modulus under the generalized Riemann hypothesis.