The twisted fourth moment of the Riemann zeta function

TL;DR

This paper calculates the asymptotic behavior of the fourth moment of the Riemann zeta function combined with a Dirichlet polynomial of limited length, advancing understanding of zeta function moments.

Contribution

It provides the first asymptotic formula for the fourth moment of the zeta function multiplied by a Dirichlet polynomial of length up to T^{1/11 - epsilon}.

Findings

Asymptotic formula for the fourth moment with Dirichlet polynomial

Extension of moment calculations to longer Dirichlet polynomials

Improved bounds on moments of the Riemann zeta function

Abstract

We compute the asymptotics of the fourth moment of the Riemann zeta function times an arbitrary Dirichlet polynomial of length $T^{{1/11} - \epsilon}$