The modified Mellin transform Zk(s) = ∫ ∞ 1 |ζ( 1 2 + ix)|x dx (k ∈ N) is investigated. Analytic continuation and mean square estimates of Zk(s) are discussed, as well as connections with power moments of |ζ( 1 2 +ix)|, with the special emphasis on the cases k = 1, 2.

It is shown that the space of finite-to-finite holomorphic correspondences on an OT-manifold is discrete. When the OT-manifold has no proper infinite complex-analytic subsets, it then follows by known model-theoretic results that its cartesian powers have no interesting complex-analytic families of subvarieties. The methods of proof, which are similar to [Moosa, Moraru, and Toma “An essentially...