Moments of zeta and correlations of divisor-sums: III

J B Conrey; Jon P Keating

doi:10.1016/j.indag.2015.04.005

Moments of zeta and correlations of divisor-sums: III

J B Conrey, Jon P Keating

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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 language	English
Pages (from-to)	736-747
Number of pages	12
Journal	Indagationes Mathematicae
Volume	26
Issue number	5
DOIs	https://doi.org/10.1016/j.indag.2015.04.005
Publication status	Published - 1 Dec 2015

Keywords

Divisor correlations
Moments
Random matrix theory
Riemann zeta-function

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10.1016/j.indag.2015.04.005

1-s2.0-S0019357715000385-main
(C) 2015 The Authors. Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG). This is an open access article under the CC BY license.
Final published version, 185 KBLicence: CC BY

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title = "Moments of zeta and correlations of divisor-sums: III",

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.",

keywords = "Divisor correlations, Moments, Random matrix theory, Riemann zeta-function",

author = "Conrey, \{J B\} and Keating, \{Jon P\}",

year = "2015",

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language = "English",

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journal = "Indagationes Mathematicae",

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TY - JOUR

T1 - Moments of zeta and correlations of divisor-sums

T2 - III

AU - Conrey, J B

AU - Keating, Jon P

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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.

KW - Divisor correlations

KW - Moments

KW - Random matrix theory

KW - Riemann zeta-function

UR - https://www.scopus.com/pages/publications/84947612730

U2 - 10.1016/j.indag.2015.04.005

DO - 10.1016/j.indag.2015.04.005

M3 - Article (Academic Journal)

AN - SCOPUS:84947612730

SN - 0019-3577

VL - 26

SP - 736

EP - 747

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 5

ER -

Moments of zeta and correlations of divisor-sums: III

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Moments of zeta and correlations of divisor-sums: IV

L-functions and modular forms

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Moments of zeta and correlations of divisor-sums: III

Abstract

Keywords

Access to Document

Handle.net

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Embargoed Document

Fingerprint

Research output

Moments of zeta and correlations of divisor-sums: IV

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L-functions and modular forms

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