Higher moments of distribution of zeta zeros

TL;DR

This paper introduces a new method for estimating mean-values of long Dirichlet polynomials and applies it to analyze the properties of the logarithmic derivative of the Riemann zeta function.

Contribution

A novel approach for mean-value estimation of Dirichlet polynomials and its application to zeta function analysis.

Findings

Established properties of the logarithmic derivative of the Riemann zeta function

Developed a new method for mean-value estimation of Dirichlet polynomials

Enhanced understanding of zeta zeros distribution

Abstract

We develop a method for mean-value estimation of long Dirichlet polynomials. For an application, we use our method to study properties of the logarithmic derivative of the Riemann zeta function.