Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-17T16:21:28.023Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

Abstract

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.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 1: Special issue dedicated to the 13th "Journées Montoises d'Informatique Théorique" , January 2012 , pp. 87 - 106
Copyright
© EDP Sciences 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Références

Akiyama, S., Frougny, Ch. and Sakarovitch, J., Powers of rationals modulo 1 and rational base number systems. Isr. J. Math. 168 (2008) 53–91. Google Scholar
Kátai, I. and Szabó, J., Canonical number systems for complex integers. Acta Sci. Math. (Szeged) 37 (1975) 255–260. Google Scholar
M. Lothaire, Algebraic Combinatorics on Words, Encyclopedia of Mathematics and its Applications 95. Cambridge University Press (2002).
Mahler, K., An unsolved problem on the powers of 3/2. J. Austral. Math. Soc. 8 (1968) 313–321. Google Scholar
M.R. Murty, Introduction to p-adic analytic number theory. American Mathematical Society (2002).
Odlyzko, A. and Wilf, H., Functional iteration and the Josephus problem. Glasg. Math. J. 33 (1991) 235–240. Google Scholar
Rényi, A., Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungar. 8 (1957) 477–493. Google Scholar
Robinson, W.J., The Josephus problem. Math. Gaz. 44 (1960) 47–52. Google Scholar
J. Sakarovitch, Elements of Automata Theory. Cambridge University Press, New York (2009).