Moments of zeta and correlations of divisor-sums: I

Brian Conrey; Jonathan P. Keating

doi:10.1098/rsta.2014.0313

Moments of zeta and correlations of divisor-sums: I

Brian Conrey^*
, Jonathan P. Keating

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

34 Citations (Scopus)

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Abstract

We examine the calculation of the second and fourth moments and shifted moments of the Riemann zetafunction on the critical line using long Dirichlet polynomials and divisor correlations. Previously, this approach has proved unsuccessful in computing moments beyond the eighth, even heuristically. A careful analysis of the second and fourth moments illustrates the nature of the problem and enables us to identify the terms that are missed in the standard application of these methods.

Original language	English
Article number	20140313
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	373
Issue number	2040
DOIs	https://doi.org/10.1098/rsta.2014.0313
Publication status	Published - 23 Mar 2015

Keywords

Divisor-sums
Moments
Random matrix theory
Riemann zeta-function

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10.1098/rsta.2014.0313

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via The Royal Society at DOI: 10.1098/rsta.2014.0313. Please refer to any applicable terms of use of the publisher.
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AB - We examine the calculation of the second and fourth moments and shifted moments of the Riemann zetafunction on the critical line using long Dirichlet polynomials and divisor correlations. Previously, this approach has proved unsuccessful in computing moments beyond the eighth, even heuristically. A careful analysis of the second and fourth moments illustrates the nature of the problem and enables us to identify the terms that are missed in the standard application of these methods.

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KW - Moments

KW - Random matrix theory

KW - Riemann zeta-function

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AN - SCOPUS:84925433352

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Moments of zeta and correlations of divisor-sums: I

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Keywords

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