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

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.