Lower bounds for discrete moments in a conjecture of Ng

Assuming the Riemann Hypothesis and the simplicity of the non-trivial zeros of the Riemann zeta function $\zeta (s)$, we prove lower bounds for the discrete moments ${\sum }_{0<\gamma \le T}\mathrm{\mid }\zeta (2\rho )\mathrm{/}{\zeta }^{\mathrm{\prime }}(\rho ){\mathrm{\mid }}^{2k}$ for every fixed rational $k\ge 1$, and for every fixed real $k\ge 1$. At $k=1$ we give a new proof of the explicit bound, half of the main term conjectured by Ng.