Proof of the Riemann Hypothesis

TL;DR

This paper claims to prove the Riemann hypothesis by analyzing the integral representation of the zeta function and solving it to show that all non-trivial zeros have real part 1/2, addressing a major open problem in number theory.

Contribution

It presents a purported proof of the Riemann hypothesis using integral analysis of the zeta function's representation, which is a novel approach.

Findings

Claims to prove the Riemann hypothesis.

Shows that the zeros of the zeta function lie on the critical line.

Provides a new integral-based method for analyzing the zeta function.

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.