Reprint: An unsolved problem on the powers of \(3/2\) (1968)
type: Item
instance of: scholarly article
title: Reprint: An unsolved problem on the powers of \(3/2\) (1968)
zbMATH Open document ID: 1457.11003
published in: Documenta Mathematica
publication date: 2021-03-05T00:00:00Z
review text: Summary: One says that \(\alpha>0\) is a \(Z\)-number if \(0\le \{\alpha (3/2)^n\}<1/2\), where \(\{x\}\) denotes the fractional part of \(x\). In this paper, while not showing existence, Mahler proves that the set of \(Z\)-numbers is at most countable. More specifically, Mahler shows that, up to \(x\), there are at most \(x^{0.7} Z\)-numbers. Reprint of the author's paper [J. Aust. Math. Soc. 8, 313--321 (1968; Zbl 0155.09501)].
Mathematics Subject Classification ID: 11-03
Mathematics Subject Classification ID: 11J54
zbMATH DE Number: 7317830
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/dms/8/39
OpenAlex ID: W4361793087
DOI: 10.4171/DMS/8/39
author: Kurt Mahler
description: scientific article; zbMATH DE number 7317830