Non trivial zeros of the Zeta function using the differential equations
Résumé
Using the differential equations, we obtain a more flexible expression for the Riemann Zeta function on the right half-plan except the point $s=1$. Thanks to the Riemann functional equation, we suggest that the point $s \in \mathbb{C}$ such that $\Re(s)\in (0,2^{-1}]$ is a non-trivial zero of the function $\zeta$ implies $|s^2\Gamma(s)|\geq |(1-s)^2\Gamma(1-s)|$, where $\Gamma$ is the Gamma function.
Domaines
Mathématiques générales [math.GM]
Origine : Fichiers produits par l'(les) auteur(s)