Distribution of \({\mathcal B}\)-free numbers in short intervals
type: Item
instance of: scholarly article
title: Distribution of \({\mathcal B}\)-free numbers in short intervals
zbMATH Open document ID: 0790.11068
author: Jie Wu
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1994-06-26T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/93569
review text: The author gives a brief survey of results on \(\mathcal B\)-free numbers, up to and including the result described in the preceding review, before considering the solubility of the equations \(p+ k= a\), \(n=p+ a\), where \(p\) denotes a prime and \(a\) a \(\mathcal B\)-free number. The new result is that these have solutions with \(p\) between \(n\) and \(n- n^ \theta\), whenever \(\theta>3/4\) and \(n\) is large enough (given a necessary condition mod 2 when \(n\) is even). The proof is supplied for the equation \(p+ k= a\), where (as in the author's previous theorem) the result embodies a quantitative lower bound of the correct order of magnitude, in this instance for the number of primes \(p\) involved.
reviewed by: George Greaves
Mathematics Subject Classification ID: 11N25
Mathematics Subject Classification ID: 11P32
zbMATH DE Number: 484168
zbMATH Keywords: brief survey
zbMATH Keywords: \(\mathcal B\)-free numbers
MaRDI profile type: Publication
OpenAlex ID: W2507522457
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cites work: Nombres
DOI: 10.5802/JTNB.85
description: scientific article; zbMATH DE number 484168