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arXiv · 1804.08826

An upper bound for discrete moments of the derivative of the Riemann zeta-function

Scott Kirila
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Abstract

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

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Scott Kirila. 2018-04-24. An upper bound for discrete moments of the derivative of the Riemann zeta-function. https://doi.org/10.1112/mtk.12008

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