On an effective order estimate of the Riemann zeta function in the critical strip
type: Item
instance of: scholarly article
title: On an effective order estimate of the Riemann zeta function in the critical strip
zbMATH Open document ID: 0713.11060
DOI: 10.1007/BF01320691
published in: Monatshefte für Mathematik
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178474
review text: The well-known explicit estimation of the order of the Riemann zeta function \[ | \zeta (\sigma +it)| \ll t^{c(1-\sigma)^{3/2}} \ln^{2/3}t \] for 1/2\(\leq \sigma \leq 1\) and \(t\geq 2\) [see \textit{H. E. Richert}, Math. Ann. 169, 97-101 (1967; Zbl 0161.048)] is proved with the constant \(c=21\). The improvement of the constant c is a consequence of some technical modifications in application of the Vinogradov's inequality for exponential sums with the constant improved by \textit{E. I. Panteleeva} [Mat. Zametki 44, 494-505 (1988); Engl. translation in Math. Notes 44, 750-757 (1988; Zbl 0654.10041)].
Mathematics Subject Classification ID: 11M26
Mathematics Subject Classification ID: 11L07
zbMATH DE Number: 4173113
zbMATH Keywords: order of the Riemann zeta function
zbMATH Keywords: Vinogradov's inequality
zbMATH Keywords: exponential sums
author: Krystyna Maria Bartz
MaRDI profile type: Publication
cites work: Zur Abschätzung der Riemannschen Zetafunktion in der Nähe der Vertikalen \(\sigma = 1\)
cites work: Q5803461
cites work: Q5636969
description: scientific article; zbMATH DE number 4173113