Properties of the function \(f(x) = x/\pi(x)\)
type: Item
instance of: scholarly article
title: Properties of the function \(f(x) = x/\pi(x)\)
zbMATH Open document ID: 1049.11100
DOI: 10.1155/S0161171201005725
author: Panayiotis Vlamos
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/50993
review text: In this paper the author proves asymptotic expansions for \(\sum_{k=2}^n f(k)\) and \(\sum_{k=2}^n 1/f(k)\), where \(f(k) = k/\pi(k)\), \(k \geq 2\). He studies the expression \(2f(x+y)-f(x)-f(y)\) for integers \(x,y \geq 2\) and as an application gives several remarks in connection with the Hardy-Littlewood conjecture.
Mathematics Subject Classification ID: 11N05
Mathematics Subject Classification ID: 11A25
zbMATH DE Number: 1780270
zbMATH Keywords: asymptotic series expansions
reviewed by: Olaf Ninnemann
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1780270