Moments of zeta and correlations of divisor-sums: IV

Brian Conrey, Jon P Keating

Research output: Contribution to journalArticle (Academic Journal)

8 Citations (Scopus)
284 Downloads (Pure)

Abstract

In this series 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 begins 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 length up to T3 with divisor functions as coefficients.
Original languageEnglish
Article number24
Number of pages24
JournalResearch in Number Theory
Volume2
Early online date21 Nov 2016
DOIs
Publication statusPublished - Dec 2016

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