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Moments of zeta and correlations of divisor-sums: I

Research output: Contribution to journalArticle

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


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.

    Research areas

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

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    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via The Royal Society at DOI: 10.1098/rsta.2014.0313. Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 265 KB, PDF document


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