Article (Scientific journals)
Abstract beta-expansion and ultimately periodic representations
Rigo, Michel; Steiner, Wolfgang
2005In Journal de Théorie des Nombres de Bordeaux, 17, p. 288-299
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Keywords :
Abstract numeration system; Pisot number; beta-expansion
Abstract :
[en] For abstract numeration systems built on exponential regular languages (including those coming from substitutions), we show that the set of real numbers having an ultimately periodic representation is $\mathbb{Q}(\beta)$ if the dominating eigenvalue $\beta>1$ of the automaton accepting the language is a Pisot number. Moreover, if $\beta$ is neither a Pisot nor a Salem number, then there exist points in $\mathbb{Q}(\beta)$ which do not have any ultimately periodic representation.
Disciplines :
Mathematics
Author, co-author :
Rigo, Michel  ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Steiner, Wolfgang
Language :
English
Title :
Abstract beta-expansion and ultimately periodic representations
Publication date :
2005
Journal title :
Journal de Théorie des Nombres de Bordeaux
ISSN :
1246-7405
Publisher :
Université de Bordeaux III, France
Volume :
17
Pages :
288-299
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 01 July 2009

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