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Rational base number systems for p-adic numbers

  • Christiane Frougny (a1) and Karel Klouda (a2)
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.

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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

S. Akiyama , Ch. Frougny and J. Sakarovitch , Powers of rationals modulo 1 and rational base number systems. Isr. J. Math. 168 (2008) 5391.

K. Mahler , An unsolved problem on the powers of 3/2. J. Austral. Math. Soc. 8 (1968) 313321.

A. Odlyzko and H. Wilf , Functional iteration and the Josephus problem. Glasg. Math. J. 33 (1991) 235240.

A. Rényi , Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungar. 8 (1957) 477493.

W.J. Robinson , The Josephus problem. Math. Gaz. 44 (1960) 4752.

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RAIRO - Theoretical Informatics and Applications
  • ISSN: 0988-3754
  • EISSN: 1290-385X
  • URL: /core/journals/rairo-theoretical-informatics-and-applications
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