6. Making the method more rigorous

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.
Remark. For this problem, it may be easier to start with low moments first.


Problem 6.2.
[H. Iwaniec] Is there some version of MoĢbius 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 HardyLittlewood for the probability that both $n$ and $n+h$ are prime)? 
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.