Rational base number systems for \(p\)-adic numbers
type: Item
instance of: scholarly article
zbMATH Open document ID: 1338.11010
author: Karel Klouda
author: Christiane Frougny
publication date: 2012-08-31T00:00:00Z
full work available at URL: https://eudml.org/doc/221988
Mathematics Subject Classification ID: 11A67
Mathematics Subject Classification ID: 11S99
zbMATH DE Number: 6074745
zbMATH Keywords: \(p\)-adic numbers
zbMATH Keywords: rational base number systems
MaRDI profile type: Publication
OpenAlex ID: W2165696329
cites work: Powers of rationals modulo 1 and rational base number systems
cites work: Q4529547
cites work: An unsolved problem on the powers of 3/2
cites work: Q4552287
cites work: Functional iteration and the Josephus problem
cites work: Representations for real numbers and their ergodic properties
cites work: Q3644388
DOI: 10.1051/ITA/2011114
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title: Rational base number systems for \(p\)-adic numbers
published in: RAIRO. Theoretical Informatics and Applications
review text: This paper is concerned with rational base number systems for \(p\)-adic numbers, in particular with those introduced in [\textit{S. Akiyama} et al., Isr. J. Math. 168, 53--91 (2008; Zbl 1214.11089)]. The authors identify those numbers which have finite and eventually periodic representations, and they determine the number of representations of a given \(p\)-adic number. Moreover, the authors investigate the relation between this number system and three other rational base number systems for \(p\)-adic numbers, and show that they all are in some sense isomorphic and share most of their properties.
reviewed by: Christoph Aistleitner
description: scientific article; zbMATH DE number 6074745