Riemann's Functional Equation is Not Valid and its Implication on the Riemann Hypothesis

Abstract

Riemann’s “functional” equation was formulated by Riemann that supposedly extended the domain of the Riemann zeta function from the right half-plane into the entire complex plane except at z = 1. It is also the foundation upon which the Riemann Hypothesis is based: that all the zeros of the zeta function are at z = 1⁄2 + iy. But the equation, as shall be shown here is not valid such that the Riemann Hypothesis crumbles on its claim.