Note on the sum of cubes of primes and an almost prime
type: Item
instance of: scholarly article
title: Note on the sum of cubes of primes and an almost prime
zbMATH Open document ID: 0882.11057
author: Koichi Kawada
published in: Archiv der Mathematik
publication date: 1997-08-27T00:00:00Z
review text: Let \(E(N)\) be the number of positive integers \(n\in\mathbb{N}\) \((n\equiv 0(2)\), \(n\not\equiv\pm1,\pm3(9)\), \(n\not\equiv\pm 1(7))\) which are not representable in the form \(n= P^3_3+ p^3_1+p^3_2+ p^3_3\) (\(p_1\), \(p_2\), \(p_3\) denote primes, \(P_r\) denotes positive integers with at most \(r\) prime factors). It is shown that \(E(N)\ll N(\log N)^{-A}\) for any fixed \(A>0\). The proof follows the method of \textit{J. Brüdern} [Ann. Sci. Éc. Norm. Supér., IV. Sér. 28, No. 4, 461-476 (1995; Zbl 0839.11045)], where the same result was gained with \(P_4\) instead of \(P_3\). The improvement is achieved by a different use of the linear sieve.
Mathematics Subject Classification ID: 11P32
Mathematics Subject Classification ID: 11N36
Mathematics Subject Classification ID: 11P55
Mathematics Subject Classification ID: 11P05
zbMATH DE Number: 1052891
zbMATH Keywords: sum of cubes of primes and an almost prime
zbMATH Keywords: linear sieve
reviewed by: Dieter Wolke
MaRDI profile type: Publication
full work available at URL: s000130050088
OpenAlex ID: W2024857882
DOI: 10.1007/S000130050088
description: scientific article; zbMATH DE number 1052891