An Upper Bound for Discrete Moments of the Derivative of the Riemann Zeta‐function

Assuming the Riemann hypothesis, we establish an upper bound for the 2kth discrete moment of the derivative of the Riemann zeta-function at nontrivial zeros, where k is a positive real number. Our upper bound agrees with conjectures of Gonek and Hejhal and of Hughes, Keating and O'Connell. This sharpens a result of Milinovich. Our proof builds upon a method of Adam Harper concerning continuous moments of the zeta-function on the critical line.