Decoupling for perturbed cones and mean square of $|\zeta(\frac 12+it)|$

TL;DR

This paper improves estimates for the mean square of the Riemann zeta function on the critical line using advanced decoupling techniques from harmonic analysis.

Contribution

It introduces a novel application of decoupling methods to refine bounds on the zeta function's mean square, advancing analytical number theory.

Findings

Enhanced bounds for the mean square of |rac{1}{2}+it|

Application of harmonic analysis decoupling techniques

Potential implications for the distribution of zeros

Abstract

An improved estimate is obtained for the mean square of the modulus of the zeta function on the critical line. It is based on the decoupling techniques in harmonic analysis developed in [B-D]