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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 MoĢˆbius 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.