
## 1. Divisor sums

1. ### 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 $H$.
1. Remark. [K. Soundararajan] Find connections with the paper of Keating, Rodgers, Roditty-Gershon, 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, 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.