Moments of zeta and correlations of divisor-sums: IV

Brian Conrey; Jon P Keating

doi:10.1007/s40993-016-0056-4

Moments of zeta and correlations of divisor-sums: IV

Brian Conrey, Jon P Keating

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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 language	English
Article number	24
Number of pages	24
Journal	Research in Number Theory
Volume	2
Early online date	21 Nov 2016
DOIs	https://doi.org/10.1007/s40993-016-0056-4
Publication status	Published - Dec 2016

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21 Citations
2 Article (Academic Journal)
1 Chapter in a book

Moments of zeta and correlations of divisor-sums: III
Conrey, J. B. & Keating, J. P., 1 Dec 2015, In: Indagationes Mathematicae. 26, 5, p. 736-747 12 p.
Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Moments of zeta and correlations of divisor-sums: II
Conrey, B. & Keating, J. P., 2015, Fields Institute Communications. Springer, New York, NY, Vol. 77. p. 75-85 11 p. (Fields Institute Communications; vol. 77).
Research output: Chapter in Book/Report/Conference proceeding › Chapter in a book
23 Citations (Scopus)
Moments of zeta and correlations of divisor-sums: I
Conrey, B. & Keating, J. P., 23 Mar 2015, In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 373, 2040, 20140313.
Research output: Contribution to journal › Article (Academic Journal) › peer-review

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L-functions and modular forms
Keating, J. P. (Co-Principal Investigator) & Booker, A. R. (Principal Investigator)
1/06/13 → 30/09/19
Project: Research

Cite this

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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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Moments of zeta and correlations of divisor-sums: IV

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Moments of zeta and correlations of divisor-sums: III

Moments of zeta and correlations of divisor-sums: II

Moments of zeta and correlations of divisor-sums: I

Projects

L-functions and modular forms

Cite this