One inequality involving simple zeros of ζ(s)\zeta(s).

International audienceLet $\rho = \beta + i \gamma$ denote a non-trivial zero of the Riemann zeta-function $\zeta(s)$. It is shown unconditionally that :$$\sum^{} \limits_{|\gamma| < T} \frac {1}{\left | \rho \zeta^{\prime}(\rho) \right |} \gg (\log T)^{3/4},$$where the sum runs over the simple zeros of $\zeta(s)$. This improves an earlier quantitative result of the sum under consideration