  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.
