An explicit upper bound for the Riemann zeta-function near the line \(\omega=1\)
type: Item
instance of: scholarly article
title: An explicit upper bound for the Riemann zeta-function near the line \(\omega=1\)
zbMATH Open document ID: 0928.11034
author: K. Appert
published in: Rocky Mountain Journal of Mathematics
publication date: 1999-11-30T00:00:00Z
full work available at URL: CONT29-1.html
review text: The author proves the bounds \[ | \zeta(\sigma + it)| \leq 175t^{146(1-\sigma)^{3/2}}\log^{2/3}t \quad({\textstyle{1\over 2}} \leq \sigma \leq 1, t \geq 2) \] and \[ | \zeta(\sigma + it)| \leq 175\log^{2/3}t \qquad(\sigma \geq 1, t \geq 2). \] The merit of these results is that the numerical constants are all explicit, for otherwise the bounds are well-known. The proofs are based on careful, laborious estimations involving the known proofs. Each step of the proof is explicitly worked out.
Mathematics Subject Classification ID: 11M06
zbMATH DE Number: 1309612
zbMATH Keywords: Riemann zeta-function
zbMATH Keywords: methods of Korobov and Vinogradov
zbMATH Keywords: Euler summation formula
reviewed by: Aleksandar Ivić
MaRDI profile type: Publication
OpenAlex ID: W2003056945
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DOI: 10.1216/RMJM/1181071682
description: scientific article; zbMATH DE number 1309612