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1. Divisor sums

    1. Moments of divisor functions in short intervals


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      Problem 1.1.

      [S. Lester] Evaluate $$\int_X^{2X} \left| \sum_{x\leq n\leq x+H} d_k(n) \ - \ \mbox{main term}\right|^{2\ell}\,dx$$ for different ranges of $H$.
        1. Remark. [K. Soundararajan] Find connections with the paper of Keating, Rodgers, Roditty-Gershon, and Rudnick.


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              Problem 1.2.

              [B. Rodgers] Some coefficients of the Ramanujan tau function appear as coefficients of the piecewise polynomial in the work of Keating, Rodgers, Roditty-Gershon, and Rudnick. Is this a coincidence or not?

                  Cite this as: AimPL: Moments of zeta and correlations of divisor sums, available at http://aimpl.org/zetamoments.