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Assuming the Riemann hypothesis, we establish an upper bound for the 2 k th 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.

AN UPPER BOUND FOR DISCRETE MOMENTS OF THE DERIVATIVE OF THE RIEMANN ZETA‐FUNCTION