Moments of zeta and correlations of divisor-sums: I

Brian Conrey*, Jonathan P. Keating

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

27 Citations (Scopus)
298 Downloads (Pure)


We examine the calculation of the second and fourth moments and shifted moments of the Riemann zetafunction on the critical line using long Dirichlet polynomials and divisor correlations. Previously, this approach has proved unsuccessful in computing moments beyond the eighth, even heuristically. A careful analysis of the second and fourth moments illustrates the nature of the problem and enables us to identify the terms that are missed in the standard application of these methods.

Original languageEnglish
Article number20140313
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2040
Publication statusPublished - 23 Mar 2015


  • Divisor-sums
  • Moments
  • Random matrix theory
  • Riemann zeta-function


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