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Publication - Professor Jon Keating

    Moments of zeta and correlations of divisor-sums

    IV

    Citation

    Conrey, B & Keating, JP, 2016, ‘Moments of zeta and correlations of divisor-sums: IV’. Research in Number Theory, vol 2.

    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.

    Full details in the University publications repository