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Moments of zeta and correlations of divisor-sums: IV

Research output: Contribution to journalArticle

Original languageEnglish
Article number24
Number of pages24
JournalResearch in Number Theory
Volume2
Early online date21 Nov 2016
DOIs
DateAccepted/In press - 29 Aug 2016
DateE-pub ahead of print - 21 Nov 2016
DatePublished (current) - Dec 2016

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.

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    Rights statement: This is the final published version of the article (version of record). It first appeared online via Springer at http://link.springer.com/article/10.1007/s40993-016-0056-4. Please refer to any applicable terms of use of the publisher.

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