The fourth moment of individual Dirichlet L-functions on the critical line

TL;DR

This paper derives an asymptotic formula for the second moment of a product of Dirichlet L-functions on the critical line, providing new uniform results including the fourth moment of individual Dirichlet L-functions.

Contribution

It introduces a power-saving asymptotic formula for the second moment of Dirichlet L-functions, extending to special cases like Dedekind zeta functions of quadratic fields.

Findings

Power-saving error term in the second moment formula

Uniform asymptotic formulas for Dirichlet L-functions

Results applicable to Dedekind zeta functions of quadratic fields

Abstract

We prove an asymptotic formula for the second moment of a product of two Dirichlet L-functions on the critical line, which has a power saving in the error term and which is uniform with respect to the involved Dirichlet characters. As special cases we give uniform asymptotic formulae for the fourth moment of individual Dirichlet L-functions and for the second moment of Dedekind zeta functions of quadratic number fields on the critical line.