Authors: Abdelmajid Ben Hadj Salem
In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called Riemann Hypothesis : The nontrivial roots (zeros) $s=\sigma+it$ of the zeta function, defined by: $$\zeta(s) = \sum_{n=1}^{+\infty}\frac{1}{n^s},\,\mbox{for}\quad \Re(s)>1$$ have real part $\sigma= 1/2$. We give a proof that $\sigma= 1/2$ using an equivalent statement of the Riemann Hypothesis concerning the Dirichlet $\eta$ function.
Comments: 9 Pages. Submitted to the Arabian Journal of Mathematics. Comments welcome.
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