Additive problems for integers with a given number of prime divisors
type: Item
instance of: scholarly article
title: Additive problems for integers with a given number of prime divisors
zbMATH Open document ID: 0923.11131
DOI: 10.1007/BF02312848
author: M. B. Khripunova
published in: Mathematical Notes
publication date: 1999-04-11T00:00:00Z
review text: Asymptotic estimates of sums of the form \[ \sum_{n<N, \omega (n)=k} r\bigl(| b\cdot n-a|\bigr)\tag{1} \] is studied, where \(\omega(n)\) is the number of distinct prime divisors of \(n\), and \(r(n)\) is the number of all divisors. For \(a=N\), \(b=1\), in finding the asymptotics of the sum (1), we obtain the asymptotics of the number of solutions of the equation \(N=n+x\cdot y\), where \(\omega(n)=k\) and \(x,y\) are integers; for \(b=1\), we obtain the asymptotics of the number of solutions of the equation \(a= n-x \cdot y\), where \(n<N\), \(\omega(n)=k\), and \(x,y\) are integers.
Mathematics Subject Classification ID: 11N37
zbMATH DE Number: 1262506
zbMATH Keywords: number of divisors
zbMATH Keywords: number of distinct prime divisors
zbMATH Keywords: asymptotic results
reviewed by: A. Yu. Timofeev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02312848
OpenAlex ID: W2036268532
description: scientific article; zbMATH DE number 1262506