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Moments of zeta and correlations of divisor-sums: III

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)736-747
Number of pages12
JournalIndagationes Mathematicae
Issue number5
DateAccepted/In press - 1 Jan 2015
DatePublished (current) - 1 Dec 2015


In this series we examine the calculation of the 2k2kth moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper is concerned with the precise input of the conjectural formula for the classical shifted convolution problem for divisor sums so as to obtain all of the lower order terms in the asymptotic formula for the mean square along [T,2T][T,2T] of a Dirichlet polynomial of length up to T2T2 with divisor functions as coefficients.

    Research areas

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

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  • 1-s2.0-S0019357715000385-main

    Rights statement: (C) 2015 The Authors. Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG). This is an open access article under the CC BY license.

    Final published version, 185 KB, PDF document

    Licence: CC BY


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