
## 6. Making the method more rigorous

1. #### Problem 6.1.

[S. Bettin] Can one formulate a conjecture (e.g. Kloosterman sum estimates) that lead to the calculations of Conrey and Keating in a rigorous way? We need a better understanding (even mechanically) of these calculations.
1. Remark. For this problem, it may be easier to start with low moments first.
• #### Problem 6.2.

[H. Iwaniec] Is there some version of Möbius randomness that would lead to similar calculations? And vice versa, can one go back to primes e.g. from analogs for ratios conjectures?
• #### Problem 6.3.

[B. Rodgers] Is there a random model on the primes that leads to the Type II calculations of Bogomolny and Keating (e.g. use Hardy-Littlewood for the probability that both $n$ and $n+h$ are prime)?
• #### Problem 6.4.

[A. Harper] Can we make the calculations uniform in $k$?
• #### Problem 6.5.

[H. Iwaniec] Can one formulate a weighted version of moments with potentially simpler main terms?

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