Solution de l'Hypoth\`ese de Riemann

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.