Hardy-Littlewood numbers in short intervals
type: Item
instance of: scholarly article
title: Hardy-Littlewood numbers in short intervals
zbMATH Open document ID: 0851.11056
published in: Journal of Number Theory
publication date: 1996-11-25T00:00:00Z
review text: A positive integer \(n\) is called a Hardy-Littlewood number if it can be written as a sum of a prime and a square. A quantitative corollary of the authors' main theorem is that for \(\varepsilon\), \(A > 0\), \(N^{7/24 + \varepsilon} \leq H \leq N\), all but \(O(H (\ln N)^{- A})\) integers \(n \in \lfloor N,N + H\rfloor\) are Hardy-Littlewood numbers. The proof follows the lines of earlier papers on similar questions (the first jointly with \textit{R. Brünner}) [Acta Math. Hung. 53, 347-365 (1989; Zbl 0683.10039); J. Lond. Math. Soc., II. Ser. 47, 41-49 (1993; Zbl 0806.11042)]. The authors state that the same result was proved independently by H. Mikawa.
reviewed by: Dieter Wolke
Mathematics Subject Classification ID: 11P32
zbMATH DE Number: 809126
zbMATH Keywords: short intervals
zbMATH Keywords: Hardy-Littlewood numbers
author: A. Perelli
author: János Pintz
MaRDI profile type: Publication
full work available at URL: jnth.1995.1120
OpenAlex ID: W1966443156
DOI: 10.1006/JNTH.1995.1120
description: scientific article; zbMATH DE number 809126