Density of m-tuples with respect to polynomials
type: Item
instance of: scholarly article
title: Density of m-tuples with respect to polynomials
zbMATH Open document ID: 0618.10051
DOI: 10.1216/RMJ-1985-15-2-319
author: J. Chidambaraswamy
author: R. Sita Rama Chandra Rao
published in: Rocky Mountain Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The authors obtain asymptotic formulas for the number of m-tuples \(<x_ 1,...,x_ m>\) of integers satisfying \(0<x_ i\leq x\) and with a given value of the greatest k-th power dividing \(f_ i(x_ i)\) for \(i=1,2,...,m\), where \(f_ 1,...,f_ m\) are given nonconstant polynomials with integer coefficients. They also point out errors in a previous treatment of this subject [\textit{R. N. Buttsworth}, J. Number Theory 12, 487-498 (1980; Zbl 0443.10001)].
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 11C08
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11A25
Mathematics Subject Classification ID: 11A05
zbMATH DE Number: 4002210
zbMATH Keywords: density
zbMATH Keywords: greatest common divisor
zbMATH Keywords: asymptotic formulas
zbMATH Keywords: number of m- tuples
zbMATH Keywords: polynomials with integer coefficients
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
full work available at URL: rmj-1985-15-2-319
OpenAlex ID: W2036745900
description: scientific article; zbMATH DE number 4002210