Remark on a double-inequality for the Riemann zeta function
type: Item
instance of: scholarly article
title: Remark on a double-inequality for the Riemann zeta function
zbMATH Open document ID: 1114.11070
published in: Expositiones Mathematicae
publication date: 2006-02-02T00:00:00Z
review text: The author gives an elementary proof that, for \(x>0\), \[ (1-\delta(x))\zeta(x)+\alpha\delta(x)<\zeta(x+1)<(1-\delta(x))\zeta(x) +\beta\delta(x), \] where \(\delta(x) = 1/(2^x-1)\) and \(\alpha = \log 2 - {1\over2}\), \(\beta = {1\over2}\) are best possible constants. The lower bound improves a recent result of \textit{P. Cerone} et al. [JIPAM, J. Inequal. Pure Appl. Math. 5, No. 2, Paper No. 43, 17 p., electronic only (2004; Zbl 1070.11034)], who had the lower bound with the constant 1/8.
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 5003043
zbMATH Keywords: Riemann zeta-function
zbMATH Keywords: inequalities
author: Horst Alzer
reviewed by: Aleksandar Ivić
MaRDI profile type: Publication
full work available at URL: j.exmath.2005.01.006
OpenAlex ID: W1998453566
cites work: Q4101884
cites work: Euler and the Zeta Function
cites work: Q4821372
cites work: Q4074972
cites work: A zero-density theorem for the Riemann zeta-function
cites work: The Riemann zeta-function. Transl. from the Russian by Neal Koblitz
cites work: Q5803461
DOI: 10.1016/J.EXMATH.2005.01.006
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description: scientific article; zbMATH DE number 5003043