Solution de l'Hypothèse 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: $$ζ(s) =\displaystyle \sum_{n=1}^{+\infty}\frac{1}{n^s},\,\mbox{for}\quad \Re(s)>1$$ have real part $\alpha =\frac{1}{2}$. We give a proof that $\alpha =\frac{1}{2}$ using an equivalent statement of Riemann Hypothesis.

7 pages. In French. Minor change of the title of the article. We give a complete proof of the Hypothesis. Submitted since June 2017 to the Journal ' Annales de l'ENS'. Comments welcome