On the moments of the Riemann zeta-function near the critical line
type: Item
instance of: scholarly article
title: On the moments of the Riemann zeta-function near the critical line
zbMATH Open document ID: 0861.11049
DOI: 10.1007/BF02350362
published in: Lithuanian Mathematical Journal
publication date: 1996-10-29T00:00:00Z
review text: The author considers \[ I_k (\sigma,T) = \int^T_1 \bigl|\zeta(\sigma+it) \bigr |^{2k} dt \] for \({1\over 2} < \sigma < 1\), \(k\geq 0\) and \(T\geq 2\). He shows that \[ I_k (\sigma, T) \gg_kT \left\{\min \left(\log T, {1\over \sigma - {1\over 2}} \right) \right\}^{k^2} \] for all rational \(k\), uniformly in \(\sigma\). On the Riemann hypothesis he shows that both the above bound and the corresponding upper bound hold for all real \(k\geq 0\). In the latter case explicit constants are given. The methods follow those of the reviewer [J. Lond. Math. Soc., II. Ser. 24, 65-78 (1981; Zbl 0454.10025)] and [Q. J. Math., Oxf. II. Ser. 44, 185-197 (1993; Zbl 0798.11031)] in detail.
reviewed by: D. R. Heath-Brown
Mathematics Subject Classification ID: 11M06
zbMATH DE Number: 939532
zbMATH Keywords: fractional moments of the Riemann zeta-function near the critical line
zbMATH Keywords: Riemann hypothesis
author: Antanas Laurinčikas
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02350362
OpenAlex ID: W4247251440
description: scientific article; zbMATH DE number 939532