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Rational base number systems for p-adic numbers

Published online by Cambridge University Press:  22 August 2011

Christiane Frougny and
Karel Klouda
Christiane Frougny
Affiliation:
LIAFA, CNRS UMR 7089, Case 7014, 75205 Paris Cedex 13, and Université Paris 8, France. Christiane.Frougny@liafa.jussieu.fr
Karel Klouda
Affiliation:
Faculty of Information Technology, Kolejní 550/2, 160 00 Prague, Czech Republic; karel.klouda@fit.cvut.cz

Abstract

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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.

Keywords

Rational base number systemsp-adic numbers.

References

Références

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