  The modified Mellin transform ${\cal Z}_k(s) = \int_1^\infty
|\zeta(1/2+ix)|^{2k}x^{-s}{\rm d} x (k = 1,2,...)$ is investigated. Analytic
continuation and mean square estimates of ${\cal Z}_k(s) $ are discussed, as
well as connections with power moments of $|\zeta(1/2+ix)|$, with the special
emphasis on the cases $k = 1,2$.
