The 4.36th Moment of the Riemann Zeta-Function

The Twisted Fourth Moment of the Riemann Zeta Function

We compute the asymptotics of the fourth moment of the Riemann zeta function times an arbitrary Dirichlet polynomial of length T 1 11 −ε.

Mollifying the Riemann Zeta-function

The Theory of the Riemann Zeta-function

A new approach to the spectral theory of the fourth moment of the Riemann zeta-function

The aim of the present article is to exhibit a new proof of the explicit formula for the fourth moment of the Riemann zeta-function that was established by the second named author a decade ago. Our proof is new, particularly in that it dispenses altogether with the spectral theory of sums of Kloosterman sums that played a predominant rôle in the former proof. Our argument is, instead, built dir...

On the second moment of S(T ) in the theory of the Riemann zeta function

We assume the Riemann Hypothesis and an quantitative form of the Twin Prime Conjecture, and obtain an asymptotic formula for the second moment of S(T ) with better error term.