An inequality for multiplicative functions
type: Item
instance of: scholarly article
title: An inequality for multiplicative functions
zbMATH Open document ID: 0752.11039
DOI: 10.1016/0022-314X(92)90122-6
published in: Journal of Number Theory
publication date: 1993-01-16T00:00:00Z
review text: Let \(k\) be a positive integer and \(f\) a multiplicative function with \(0<f(p)\leq 1/k\) for all primes \(p\). The author shows that, for any squarefree integer \(n\), \[ \sum_{d\mid n} f(d)\leq(k+1)\sum_{d\mid n; d\leq n^{1/(k+1)}}f(d). \] This improves some inequalities of \textit{K. Alladi}, \textit{P. Erdős} and \textit{J. D. Vaaler} [J. Number Theory 31, 183-190 (1989; Zbl 0664.10025)].
reviewed by: Pentti Haukkanen
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11A25
zbMATH DE Number: 89653
zbMATH Keywords: divisor sums
zbMATH Keywords: multiplicative function
zbMATH Keywords: inequalities
author: Kannan Soundararajan
MaRDI profile type: Publication
cites work: Multiplicative functions and small divisors. II
full work available at URL: 0022-314x(92)90122-6
OpenAlex ID: W2026248993
description: scientific article; zbMATH DE number 89653