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April 1, 2020Mathematika13 citationsOpen Access

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

SKScott KirilaUniversity of Exeter

Key Points

  • The aim is to establish an upper bound for the discrete moment of the derivative of the Riemann zeta-function under the Riemann hypothesis.
  • Assumes the Riemann hypothesis for establishing bounds.
  • Utilizes a method by Adam Harper related to continuous moments.
  • Addresses the 2kth discrete moment at nontrivial zeros, where k is a positive real number.
  • The derived upper bound agrees with conjectures by Gonek, Hejhal, Hughes, Keating, and O'Connell.
  • Improves upon Milinovich's previous results, providing sharper estimates.

Abstract

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.

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Cite This Study

Scott Kirila (2020) studied this question.

synapsesocial.com/papers/6a1fdad31517a826fb049426https://doi.org/10.1112/mtk.12008
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