Lower Bounds for Moments of ζ′(ρ)

Assuming the generalized Riemann Hypothesis for Dirichlet L-functions, we establish lower bounds of the conjectured order of magnitude for the 2kth moment of the derivative of the Riemann zeta-function averaged over the nontrivial zeros of ζ(s) for every positive integer k. Our proof is based upon a method of Rudnick and Soundararajan that provides analogous bounds for moments of L-functions at the central point, averaged over families.