Multidimensional Selberg theorem and fluctuations of the zeta zeros via Malliavin calculus

TL;DR

This paper applies Malliavin calculus to analyze the distribution and fluctuations of the Riemann zeta zeros, providing error bounds and insights into their asymptotic behavior on the critical line.

Contribution

It introduces new error bounds for the multidimensional Selberg central limit theorem for zeta zeros using Malliavin calculus.

Findings

Error bounds for the multidimensional Selberg CLT

Insights into mesoscopic fluctuations of zeta zeros

Discussion on asymptotic behavior of zeros

Abstract

We give new contributions on the distribution of the zeros of the Riemann zeta function by using the techniques of the Malliavin calculus. In particular, we obtain the error bound in the multidimensional Selberg' s central limit theorem concerning the zeta zeros on the critical line and we discuss some consequences concerning the asymptotic behavior of the mesoscopic fluctuations of the zeta zeros.