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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.
@article{ITA_2012__46_1_87_0,
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},
volume = {46},
number = {1},
year = {2012},
doi = {10.1051/ita/2011114},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2011114/}
}
TY - JOUR AU - Frougny, Christiane AU - Klouda, Karel TI - Rational base number systems for $p$-adic numbers JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2012 SP - 87 EP - 106 VL - 46 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2011114/ DO - 10.1051/ita/2011114 LA - en ID - ITA_2012__46_1_87_0 ER -
%0 Journal Article %A Frougny, Christiane %A Klouda, Karel %T Rational base number systems for $p$-adic numbers %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2012 %P 87-106 %V 46 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2011114/ %R 10.1051/ita/2011114 %G en %F ITA_2012__46_1_87_0
Frougny, Christiane; Klouda, Karel. Rational base number systems for $p$-adic numbers. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 87-106. doi: 10.1051/ita/2011114
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