A note on the fourth moment of Dirichlet L-functions

TL;DR

This paper establishes an asymptotic formula for the fourth moment of Dirichlet L-functions averaged over primitive characters and a range of t, especially effective when the modulus q exceeds T, clarifying the order of magnitude.

Contribution

It provides the first effective asymptotic formula for the fourth moment of Dirichlet L-functions in the range where q ≥ T, previously unknown.

Findings

Asymptotic formula for the fourth moment of Dirichlet L-functions

Effective when modulus q is greater than T

Clarifies the order of magnitude in this range

Abstract

We prove an asymptotic formula for the fourth power mean of Dirichlet L-functions averaged over primitive characters to modulus q and over t\in [0,T] which is particularly effective when q \ge T. In this range the correct order of magnitude was not previously known.