# Solution de l'Hypoth\`ese de Riemann

## TL;DR

This paper claims to provide a proof of the Riemann Hypothesis by demonstrating that all nontrivial zeros of the zeta function have real part 1/2, addressing a long-standing mathematical conjecture.

## Contribution

The paper presents a proof of the Riemann Hypothesis based on an equivalent formulation of the conjecture, claiming to resolve a major open problem in mathematics.

## Key findings

- Proof that all nontrivial zeros have real part 1/2
- Validation of the Riemann Hypothesis
- Advancement in understanding the zeta function zeros

## Abstract

In 1859, Riemann had announced the following conjecture : the nontrivial roots (zeros) $s=\alpha+i\beta$ of the zeta function, defined by: $$\zeta(s) =\displaystyle \sum_{n=1}^{+\infty}\frac{1}{n^s},\,\mbox{for}\quad \Re(s)>1$$ have real part $\alpha= \displaystyle \frac{1}{2}$. We give a proof that $\alpha= \displaystyle \frac{1}{2}$ using an equivalent statement of Riemann Hypothesis.