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 $ζ(s)$, we prove lower bounds for the discrete moments $\sum_{0<γ\le T}|ζ(2ρ)/ζ'(ρ)|^{2k}$ for every fixed rational $k\ge1$, and for every fixed real $k\ge1$. At $k=1$ we give a new proof of the