The Waring-Goldbach problem: one square and five cubes
type: Item
instance of: scholarly article
title: The Waring-Goldbach problem: one square and five cubes
zbMATH Open document ID: 1304.11121
author: Yingchun Cai
published in: The Ramanujan Journal
publication date: 2014-09-26T00:00:00Z
review text: Suppose that \(p_1, p_2, p_3, p_4, p_5\) are prime numbers and a natural number \(x\) has at most 36 prime factors, counted according to multiplicity. Let \(R(N)\) denote the number of solutions of the following equation \[ N=x^2+p_1^3+p_2^3+p_3^3+p_4^3+p_5^3. \] The author proves that \[ R(N)\geq c\, N^{\frac{19}{18}}/(\log N)^6, \] for an even and sufficiently large integer \(N\) with some absolute constant \(c\).
reviewed by: Jonas Šiaulys
Mathematics Subject Classification ID: 11P32
Mathematics Subject Classification ID: 11N36
zbMATH DE Number: 6348373
zbMATH Keywords: Waring-Goldbach problem
zbMATH Keywords: Hardy-Littlewood method
zbMATH Keywords: almost prime number
zbMATH Keywords: sieve method
zbMATH Keywords: number of solutions
zbMATH Keywords: lower bound
MaRDI profile type: Publication
full work available at URL: s11139-013-9486-y
OpenAlex ID: W2075180592
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DOI: 10.1007/S11139-013-9486-Y
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description: scientific article; zbMATH DE number 6348373