The fourth moment of ζ^'(ρ)

2003/10/23 by Nathan Ng, Ng, Nathan
Mathematics · #11M26 #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M26

paper · pdf · doi:10.48550/arxiv.math/0310382

arxiv created 2003/10/23 · openalex publication_date 2003/10/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Discrete moments of the Riemann zeta function were studied by Gonek and Hejhal in the 1980's. They independently formulated a conjecture concerning the size of these moments. In 1999, Hughes, Keating, and O'Connell, by employing a random matrix model, made this conjecture more precise. Subject to the Riemann hypothesis, we establish upper and lower bounds of the correct order of magnitude in the case of the fourth moment.

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