Yet another representation for the sum of reciprocals of the nontrivial zeros of the Riemann zeta-function

TL;DR

This paper presents a new representation of the sum of reciprocals of the nontrivial zeros of the Riemann zeta-function as an infinite sum with positive terms, contributing to the criteria related to the Riemann Hypothesis.

Contribution

It introduces a novel positive-summand infinite series representation for the sum of reciprocals of the zeta zeros, relevant to the Li criterion for the Riemann Hypothesis.

Findings

Sum representation as an infinite series with positive terms

Supports the positivity condition in Li's criterion

Provides a new perspective on the zeros of the Riemann zeta-function

Abstract

The positivity of the sum from the title is the first condition in the well-known criterium for the validity of the Riemann Hypothesis suggested by X.-J. Li. In the paper this value is represented as an infinite sum with positive summands.