Rational base number systems for p-adic numbers
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 46 (2012) no. 1, pp. 87-106.

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.

DOI: 10.1051/ita/2011114
Classification: 11A67,  11E95
Keywords: rational base number systems, p-adic numbers
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     author = {Frougny, Christiane and Klouda, Karel},
     title = {Rational base number systems for $p$-adic numbers},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {87--106},
     publisher = {EDP-Sciences},
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     year = {2012},
     doi = {10.1051/ita/2011114},
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Frougny, Christiane; Klouda, Karel. Rational base number systems for $p$-adic numbers. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 46 (2012) no. 1, pp. 87-106. doi : 10.1051/ita/2011114. http://www.numdam.org/articles/10.1051/ita/2011114/

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