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Moments of zeta and correlations of divisor-sums: III

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arxiv 1506.06844 v1 pith:HY55UJB3 submitted 2015-06-23 math.NT

Moments of zeta and correlations of divisor-sums: III

classification math.NT
keywords divisorcorrelationsdirichletformulamomentsshiftedalongasymptotic
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In this series 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 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 $[T,2T]$ of a Dirichlet polynomial of length up to $T^2$ with divisor functions as coefficients.

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