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Moments of zeta and correlations of divisor-sums: V

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)729-752
Number of pages24
JournalProceedings of the London Mathematical Society
Volume118
Issue number4
Early online date16 Sep 2018
DOIs
DateAccepted/In press - 23 Aug 2018
DateE-pub ahead of print - 16 Sep 2018
DatePublished (current) - 1 Apr 2019

Abstract

In this series of papers we examine the calculation of the 2kth moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper completes the general study of what we call Type II sums which utilize a circle method framework and a convolution of shifted convolution sums to obtain all of the lower order terms in the asymptotic formula for the mean square along [T; 2T] of a Dirichlet polynomial of arbitrary length with divisor functions as coeffcients.

    Research areas

  • 11M06 (primary)

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  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Wiley at https://doi.org/10.1112/plms.12196 . Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 367 KB, PDF document

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