On the density of certain sets of multiples. III
type: Item
instance of: scholarly article
title: On the density of certain sets of multiples. III
zbMATH Open document ID: 0870.11057
published in: Journal of Number Theory
publication date: 1997-06-17T00:00:00Z
review text: In Parts I and II [Acta Arith. 69, 121-152 and 171-188 (1995; Zbl 0821.11045)] the author considered the set \(B_\lambda (n)\) of integers \(m\) for which we can find a \(d \mid n\) and \(d' \mid m\) such that \(d<d'\leq ( 1 + ( \log n )^{-\lambda } ) d \), and gave asymptotic formulas, valid for almost all values of \(n\), for the density of this set. Here the quantity \(N(x, \lambda , \varepsilon )\) of those values of \(n\leq x\) is estimated for which this density is \(<1-\varepsilon \). It is proved that for \(\lambda < \log 4 -1 \) we have \[ x ( \log x )^c \leq N(x, \lambda , \varepsilon ) \leq x \exp - c' \sqrt { \log \log x} \] with certain positive constants \(c,c'\) depending on \(\lambda \).
Mathematics Subject Classification ID: 11N25
Mathematics Subject Classification ID: 11B99
zbMATH DE Number: 1011052
zbMATH Keywords: sets of multiples
zbMATH Keywords: density
author: Abdelaziz Raouj
reviewed by: Imre Z. Ruzsa
MaRDI profile type: Publication
full work available at URL: jnth.1997.2047
OpenAlex ID: W1989396372
cites work: Q5515488
cites work: On a result of R. R. Hall
cites work: Q4040373
cites work: Sur la densité de certains ensembles de multiples, 1
cites work: A Brun-Titschmarsh theorem for multiplicative functions.
cites work: Q4272975
DOI: 10.1006/JNTH.1997.2047
description: scientific article; zbMATH DE number 1011052