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arxiv: 1701.06651 · v2 · pith:C3UF6ZWYnew · submitted 2017-01-23 · 🧮 math.NT

Moments of zeta and correlations of divisor-sums: V

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keywords convolutioncorrelationsdirichletdivisormomentsshiftedsumsalong
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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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