Some remarks on the moments of $|ζ(1/2+it)|$ in short intervals

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173284Some new results on power moments of the integral $$ J_k(t,G) = {1\over\sqrtπG} \int_{-\infty}^\infty |ζ(1/2 + it + iu)|^{2k}{\rm e}^{-(u/G)^2}du \qquad(t \asymp T, T^ε\le G \ll T, k\in\N) $$ are obtained when $k=1$. These results can be used to derive bounds for moments of $|ζ(1/2+it)|$.9 pagesNumber Theory11M06, 11N37Some remarks on the moments of $|ζ(1/2+it)|$ in short intervalstext