On a problem of Erdös in additive number theory
type: Item
instance of: scholarly article
title: On a problem of Erdös in additive number theory
zbMATH Open document ID: 0858.11055
author: Dieter Wolke
published in: Journal of Number Theory
publication date: 1996-11-10T00:00:00Z
review text: A well known result of \textit{P. Erdös} [Proc. Am. Math. Soc. 5, 847-853 (1954; Zbl 0056.27001)] and \textit{G. Lorentz} [Proc. Am. Math. Soc. 5, 838-841 (1954; Zbl 0056.03902)] asserts the existence of sets \(A\) of integers with i) \(\# \{a \leq x:a\in A\} \ll \log^2 x\); ii) every sufficiently large integer \(n\) can be written as \(n=p+a\) with \(p\) prime and \(a\in A\). The author shows that there exists a set \(A\) with i)' \(\# \{a\leq x:a \in A\} \ll h(x) \log x\log \log x\), \(h(x)\) tending to \(\infty\) arbitrarily slowly; ii)' almost all integers \(n\) can be written as \(n=p + a\) with \(p\) prime and \(a\in A\).
Mathematics Subject Classification ID: 11P32
Mathematics Subject Classification ID: 11N36
zbMATH DE Number: 913837
zbMATH Keywords: additive problems with primes
reviewed by: A. Perelli
MaRDI profile type: Publication
full work available at URL: jnth.1996.0094
OpenAlex ID: W2020626706
DOI: 10.1006/JNTH.1996.0094
description: scientific article; zbMATH DE number 913837