Moments of zeta and correlations of divisor-sums: V

Brian Conrey, Jon Keating

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

15 Citations (Scopus)
272 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)729-752
Number of pages24
JournalProceedings of the London Mathematical Society
Volume118
Issue number4
Early online date16 Sept 2018
DOIs
Publication statusPublished - 1 Apr 2019

Keywords

  • 11M06 (primary)

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