The Domain of the Riemann Zeta Function on the Complex Plane

Abstract

The Riemann zeta-function is one of the most studied complex function in mathematics. Riemann in his 1859 paper On the Number of Prime Numbers less than a Given Quantity [1] claimed that the analytic continuation of the zeta-function extends its domain over the entire complex plane except at s = 1. But, as I’ve shown in my two papers: A Short Disproof of the Riemann Hypothesis [2] and Riemann’s Functional Equation is Not a Valid Function and Its Implication on the Riemann Hypothesis [3], the zeta-function is only defined on the right half-plane. It is the purpose of this present work to precisely locate the domain of this function on the right half-plane.