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

Key Points

• The aim is to establish an upper bound for the 2kth discrete moment of the derivative of the Riemann zeta-function under the assumption of the Riemann hypothesis.
• Assumed the Riemann hypothesis for analysis.
• Established the upper bound for the discrete moment at nontrivial zeros.
• Built upon Adam Harper's method regarding continuous moments on the critical line.
• The obtained upper bound aligns with Gonek and Hejhal's conjectures and Hughes, Keating, and O'Connell's conjectures.
• The result sharpens previous findings by Milinovich.