On sums of integrals of powers of the zeta-function in short intervals

dc.creatorIvić, Aleksandar
dc.date2005-12-01
dc.date2005-12-04
dc.date.accessioned2026-07-07T07:39:24Z
dc.date.available2026-07-07T07:39:24Z
dc.descriptionThe modified Mellin transform ${\cal Z}_k(s) = \int_1^\infty |ζ({1\over2}+ix|^{2k}x^{-s}{\rm d} x$ ($k\ge1$ is a fixed integer, $s = σ+ it$) is used to obtain estimates for $$ \sum_{r=1}^R\int_{t_r-G}^{t_r+G}|ζ(1/2+it)|^{2k}{\rm d} t\quad(T < t_1 < >... < t_R < 2T), $$ where $t_{r+1} - t_r \ge G (r =1,..., R-1), T^ε\le G \le T^{1-ε$. These results can be used to derive bounds for the moments of $}|ζ(1/2+it)|$.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0512016
dc.identifierhttp://arxiv.org/abs/math/0512016
dc.identifier"Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory", Proc. Symposia Pure Math. , AMS, Providence, vol. 75(2006), 231-242.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121437
dc.subjectNumber Theory
dc.subject11M06
dc.titleOn sums of integrals of powers of the zeta-function in short intervals
dc.typetext

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