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arXiv · 1701.06651

Moments of zeta and correlations of divisor-sums: V

Brian Conrey·Jonathan P. Keating
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Abstract

In this series of papers we examine the calculation of the $2k$th moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper completes 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 arbitrary length with divisor functions as coefficients.

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Brian Conrey, Jonathan P. Keating. 2018-09-03. Moments of zeta and correlations of divisor-sums: V. https://doi.org/10.1112/plms.12196

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