Proof of the Riemann Hypothesis

Abstract

The Riemann hypothesis, stating that the real part of all non-trivial zero points fo the zeta function must be $\frac{1}{2}$, is one of the most important unproven hypothesises in number theory. In this paper we will proof the Riemann hypothesis by using the integral representation $\zeta (s)=\frac{s}{s-1}-s{\int }_1^{\infty }\frac{x-\lfloor x\rfloor }{x^{s+1}}\text{d}x$ and solving the integral for the real part of the zeta function.