On a new approach to selecting the parameters of a two-dimensional sieve with weights
type: Item
instance of: scholarly article
title: On a new approach to selecting the parameters of a two-dimensional sieve with weights
zbMATH Open document ID: 0830.11034
DOI: 10.1007/BF02113305
author: A. L. Chekin
published in: Mathematical Notes
publication date: 1995-09-24T00:00:00Z
review text: The author considers a typical two-dimensional sieve problem. Let \(F\) be the product of two irreducible polynomials, \(\deg F= q\geq 3\). It is shown that \(F(n)\) is a \(P_r\) (a number with \(\leq r\) prime factors) for infinitely many \(n\) if \(r> q+\ln \ln q+ 7,27\). This is a slight improvement of a result of \textit{H. Halberstam} and \textit{H.-E. Richert} [Sieve methods (1974; Zbl 0298.10026)]. The proof uses Richert's weights. The improvement is achieved by a careful study of an integral occurring in the work of Halberstam and Richert. A similar improvement is gained for the problem of finding infinitely many primes \(p\) for which \(F(p)\) is a \(P_r\).
reviewed by: Dieter Wolke
Mathematics Subject Classification ID: 11N36
Mathematics Subject Classification ID: 11N35
Mathematics Subject Classification ID: 11N32
zbMATH DE Number: 796792
zbMATH Keywords: sieve with weights
zbMATH Keywords: almost primes presented by polynomials
zbMATH Keywords: two- dimensional sieve problem
MaRDI profile type: Publication
cites work: Selberg's sieve with weights
cites work: Q4052222
cites work: Q5559352
cites work: Some numerical results in the Selberg sieve method
full work available at URL: https://doi.org/10.1007/bf02113305
OpenAlex ID: W2078077511
description: scientific article; zbMATH DE number 796792