2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126294Power moments of $$ J_k(t,G) = {1\over\sqrtπG} \int_{-\infty}^\infty |ζ(1/2 + it + iu)|^{2k}{\rm e}^{-(u/G)^2} du \qquad(t \asymp T, T^ε\le G \ll T),$$ where $k$ is a natural number, are investigated. The results that are obtained are used to show how bounds for $\int_0^T|ζ(1/2+it)|^{2k} dt$ may be obtained.20 pagesNumber Theory11M06text