1. Divisor sums

Moments of divisor functions in short intervals
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 $H$.
Remark. [K. Soundararajan] Find connections with the paper of Keating, Rodgers, RodittyGershon, and Rudnick.


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, RodittyGershon, 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.