2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69312For a fixed integer $k\ge 3$ and fixed $1/2 < σ> 1$ we consider $$ \int_1^T |ζ(σ+ it)|^{2k}dt = \sum_{n=1}^\infty d_k^2(n)n^{-2σ}T + R(k,σ;T), $$ where $R(k,σ;T) = o(T) (T\to\infty)$ is the error term in the above asymptotic formula. Hitherto the sharpest bounds for $R(k,σ;T)$ are given for certain ranges of $σ$. We also obtain new mean value results for the zeta-functions of holomorphic cusp forms and the Rankin-Selberg series.To the memory of R.A. Rankin, 15 pagesNumber Theory11M06; 11F30; 11F66text