Rational base number systems for p-adic numbers
1 LIAFA, CNRS UMR 7089, Case 7014, 75205 Paris Cedex 13,
and Université Paris 8, France
2 Faculty of Information Technology, Kolejní 550/2, 160 00 Prague, Czech Republic
Received: 2 November 2010
Accepted: 4 July 2011
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.
Mathematics Subject Classification: 11A67 / 11E95
Key words: Rational base number systems / p-adic numbers.
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