Abdelmajid Ben Hadj Salem
Abstract
In 1898, Riemann had announced the following conjecture : 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 $\sigma= \ds \frac{1}{2}$. We give a proof that $\sigma= \ds \frac{1}{2}$ using an equivalent statement of Riemann Hypothesis.
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In 1898, Riemann had announced the following conjecture : 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 $\sigma= \ds \frac{1}{2}$. We give a proof that $\sigma= \ds \frac{1}{2}$ using an equivalent statement of Riemann Hypothesis.
Key concepts: Riemann hypothesis, Mathematics, Alternative hypothesis, Econometrics, Null hypothesis, Mathematical analysis