On the distribution of \(\alpha p\) modulo one
type: Item
instance of: scholarly article
title: On the distribution of \(\alpha p\) modulo one
zbMATH Open document ID: 0786.11042
author: Chaohua Jia
published in: Journal of Number Theory
publication date: 1994-05-09T00:00:00Z
review text: The author proves that if \(\alpha\) is an irrational number then for any real number \(\beta\) there are infinitely many primes \(p\) such that \(\| \alpha p- \beta\|< p^{-4/13}\) where, for any real \(y\), \(\| y\|= \min\{| y-n|\): \(n\in\mathbb{Z}\}\). The result improves on the previous known bound \(p^{-3/10}\) by \textit{G. Harman} [J. Lond. Math. Soc., II. Ser. 27, 9-18 (1983; Zbl 0504.10018)]. In the proof the author applies sieve methods with more delicate techniques and estimates than the previous authors.
reviewed by: Ming-Chit Liu
Mathematics Subject Classification ID: 11J71
Mathematics Subject Classification ID: 11J25
Mathematics Subject Classification ID: 11N36
zbMATH DE Number: 483986
zbMATH Keywords: distribution modulo one
zbMATH Keywords: distribution of fractional parts
zbMATH Keywords: sieve methods
MaRDI profile type: Publication
full work available at URL: jnth.1993.1075
OpenAlex ID: W2007384966
DOI: 10.1006/JNTH.1993.1075
description: scientific article; zbMATH DE number 483986