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4. Type I and type II sums


    1. Add remark

      Problem 4.1.

      [K. Soundararajan] Is there any inclusion/exclusion structure to the diagonal or type I or type II sums?
        1. Remark. An analog in Random Matrix Theory holds.


            • Add remark

              Problem 4.2.

              [T. Wooley] Why are the type II terms not already accounted for in the type I calculations? Is there a way to arrange the type I calculations to reflect these new main terms?

                • Type II sums and lattice points on lower dimensional subvarieties

                      [S. Gonek]: One of the highlights of the workshop is the link made between the appearance of Type II sums and the phenomenon of arithmetic stratification that is the subject of the Manin conjectures. As discussed by Trevor Wooley, the new insight is that the Type II terms correspond to large contributions to the divisor correlation sums used in calculating moments of long Dirichlet polynomials from counting lattice points on lower dimensional subvarieties.

                  Add remark

                  Problem 4.3.

                  Solidify this link.

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