Some remarks on the moments of left| {varsigma left( {tfrac{1}{2} + it} right)} right| in short intervals

Some new results on power moments of the integral $$ J_k (t,G) = frac{1} {{sqrt {pi G} }}int_{ - infty }^infty { left| {varsigma left( {tfrac{1} {2} + it + iu} right)} right|^{2k} } e^{ - (u/G)^2 } du $$ (t ? T, T ^? ≦ G ? T, κ ∈ N) are obtained when κ = 1. These results can be used to derive bounds for moments of $ left| {varsigma left( {tfrac{1} {2} + it} right)} right| $ .