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Beta-expansions of $p$-adic numbers

Published online by Cambridge University Press:  06 November 2014

KLAUS SCHEICHER ,
VÍCTOR F. SIRVENT  and
PAUL SURER
KLAUS SCHEICHER
Affiliation:
Institut für Mathematik, Universität für Bodenkultur, Gregor-Mendel-Straße 33, A-1180 Vienna, Austria email [email protected], [email protected]
VÍCTOR F. SIRVENT
Affiliation:
Departamento de Matemáticas, Universidad Simón Bolívar, Apartado 89000, Caracas 1086-A, Venezuela email [email protected]
PAUL SURER
Affiliation:
Institut für Mathematik, Universität für Bodenkultur, Gregor-Mendel-Straße 33, A-1180 Vienna, Austria email [email protected], [email protected]
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Abstract

In the present article, we introduce beta-expansions in the ring $\mathbb{Z}_{p}$ of $p$-adic integers. We characterise the sets of numbers with eventually periodic and finite expansions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 3 , May 2016 , pp. 924 - 943
Copyright
© Cambridge University Press, 2014 

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