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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 : IV. / Conrey, Brian; Keating, Jon P.

In: Research in Number Theory, Vol. 2, 24, 12.2016.

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Conrey, Brian ; Keating, Jon P. / Moments of zeta and correlations of divisor-sums : IV. In: Research in Number Theory. 2016 ; Vol. 2.

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@article{64ce062becf24d619d5f51a8bd789a65,
title = "Moments of zeta and correlations of divisor-sums: IV",
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.",
author = "Brian Conrey and Keating, {Jon P}",
year = "2016",
month = "12",
doi = "10.1007/s40993-016-0056-4",
language = "English",
volume = "2",
journal = "Research in Number Theory",
issn = "2363-9555",
publisher = "SpringerOpen",

}

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TY - JOUR

T1 - Moments of zeta and correlations of divisor-sums

T2 - IV

AU - Conrey, Brian

AU - Keating, Jon P

PY - 2016/12

Y1 - 2016/12

N2 - 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.

AB - 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.

U2 - 10.1007/s40993-016-0056-4

DO - 10.1007/s40993-016-0056-4

M3 - Article

VL - 2

JO - Research in Number Theory

JF - Research in Number Theory

SN - 2363-9555

M1 - 24

ER -