
## 7. Pair correlation

1. #### Problem 7.1.

[M. Radziwill] We can get lower bounds for the Type I off-diagonal terms using sifted sequences. Is there any analog of this for Type II terms? Can one improve lower bounds for $F(\alpha,T)$ in this way (as in Goldston-Gonek-Ozluk-Snyder)?
1. Remark. [K. Soundararajan] Can one get lower bounds for moments in general?
• #### Problem 7.2.

[J. Keating] Compute the $3$-point correlation function $R_3(x_1,x_2,x_3)$ for zeta rigorously under suitable hypotheses (e.g. Hardy-Littlewood conjecture for twin primes).
• #### Problem 7.3.

[J. Keating] Compute the $4$-point correlation function rigorously under suitable hypotheses (here, Type II terms come in).

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