Mathematics > Number Theory
[Submitted on 24 Apr 2018 (v1), last revised 21 Feb 2020 (this version, v2)]
Title:An upper bound for discrete moments of the derivative of the Riemann zeta-function
View PDFAbstract: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.
Submission history
From: Scott Kirila [view email][v1] Tue, 24 Apr 2018 03:09:45 UTC (15 KB)
[v2] Fri, 21 Feb 2020 14:05:10 UTC (39 KB)
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