Squares of primes and powers of 2
type: Item
instance of: scholarly article
title: Squares of primes and powers of 2
zbMATH Open document ID: 0940.11047
published in: Monatshefte für Mathematik
publication date: 2000-07-24T00:00:00Z
review text: Using the circle and sieve methods the authors show that if \(N \equiv 4\bmod 8\) and \(N\) is sufficiently large then \(N\) is representable as a sum of four squares of primes and \(k\) powers of 2, provided \(k \geq 4\). They give an asymptotic formula for the number of representations. The analogous result for a sum of two primes and at least three powers of 2 was obtained by \textit{Yu. V. Linnik} [Tr. Mat. Inst. Steklov 38, 151-169 (1951; Zbl 0049.31402) and Mat. Sb., Nov. Ser. 32, 3-60 (1953; Zbl 0051.03402)]. They also show that a positive proportion of the even numbers not exceeding \(N\) can be expressed as a sum of two squares of primes and two powers of 2. Here the corresponding result for a sum of a prime and a power of 2 is due to \textit{N. P. Romanoff} [Math. Ann. 109, 668-678 (1934; Zbl 0009.00801)].
reviewed by: George Greaves
Mathematics Subject Classification ID: 11P32
Mathematics Subject Classification ID: 11P05
Mathematics Subject Classification ID: 11N36
Mathematics Subject Classification ID: 11P55
zbMATH DE Number: 1395806
zbMATH Keywords: Goldbach problem
zbMATH Keywords: Waring problem
zbMATH Keywords: large integers
zbMATH Keywords: sum of four squares of primes and powers of two
zbMATH Keywords: asymptotic formula
zbMATH Keywords: number of representations
zbMATH Keywords: even numbers
zbMATH Keywords: sum of two squares of primes and two powers of two
author: Jianya Liu
author: Ming-Chit Liu
author: Tao Zhan
MaRDI profile type: Publication
full work available at URL: s006050050065
OpenAlex ID: W2060228350
DOI: 10.1007/S006050050065
description: scientific article; zbMATH DE number 1395806