Moments of zeta and correlations of divisor-sums: III

J B Conrey, Jon P Keating

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

12 Citations (Scopus)
308 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)736-747
Number of pages12
JournalIndagationes Mathematicae
Volume26
Issue number5
DOIs
Publication statusPublished - 1 Dec 2015

Keywords

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

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