On moments of $\mathrm{\mid }\zeta (1\mathrm{/}2+it)\mathrm{\mid }$ in short intervals

Power moments of $$J_k(t,G)=\frac{1}{\sqrt{\pi }G}{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\mathrm{\mid }\zeta (1\mathrm{/}2+it+iu){\mathrm{\mid }}^{2k}{\mathrm{e}}^{-(u\mathrm{/}G{)}^2}du(t\asymp T,T^{ϵ}\le G\ll T),$$ where $k$ is a natural number, are investigated. The results that are obtained are used to show how bounds for $\int_0^T|\zeta(1/2+it)|^{2k} dt$ may be obtained.