The twelfth moment of Dirichlet $L$-functions with smooth moduli

TL;DR

This paper extends bounds on the twelfth moment of the Riemann zeta function to Dirichlet L-functions with smooth moduli, advancing understanding of their value distribution.

Contribution

It provides an analogue of Heath-Brown's twelfth moment bound specifically for Dirichlet L-functions with smooth moduli, a novel extension in the field.

Findings

Established a new bound for the twelfth moment of Dirichlet L-functions with smooth moduli.

Extended techniques from the Riemann zeta function to a broader class of L-functions.

Contributed to the understanding of the distribution of values of Dirichlet L-functions.

Abstract

We prove an analogue of Heath-Brown's bound on the twelfth moment of the Riemann zeta function for Dirichlet L-functions with smooth moduli.