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rational base number systems

RAIRO - Theoretical Informatics and Applications (1)

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Rational base number systems for p-adic numbers
Christiane Frougny, Karel Klouda
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 46 / Issue 1 / January 2012

Published online by Cambridge University Press:

22 August 2011, pp. 87-106

Print publication:

January 2012
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This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given p-adic number.