A method for locating where the real part of the Riemann zeta function becomes negative for its real argument greater than one

TL;DR

This paper introduces an efficient search algorithm to identify points where the real part of the Riemann zeta function becomes negative for real parts greater than one, leveraging symmetries to improve performance.

Contribution

The paper presents a novel, faster algorithm for locating where the real part of the zeta function turns negative for sigma > 1, based on symmetry properties.

Findings

The algorithm significantly reduces search time compared to brute-force methods.

It successfully identifies specific points where the real part is negative.

The approach exploits symmetries in congruence equations related to the zeta function.

Abstract

This paper describes a search algorithm to locate values of t where the real part of the Riemann zeta function, zeta(sigma+it), is negative for sigma>1. The run-time to execute the search is much less than a brute-force approach and relies on certain symmetries of congruence equations related to the zeta function.