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On the beta-expansions of 1 and algebraic numbers for a Salem number beta

Published online by Cambridge University Press:  26 February 2014

HAJIME KANEKO
HAJIME KANEKO*
Affiliation:
Department of Mathematics, College of Science and Technology, Nihon University, 1-8-14 Kanda-Surugadai, Chiyoda-ku, Tokyo 101-8308, Japan email kanekoha@math.cst.nihon-u.ac.jp
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Abstract

We study the digits of $\beta $-expansions in the case where $\beta $ is a Salem number. We introduce new upper bounds for the numbers of occurrences of consecutive 0s in the expansion of 1. We also give lower bounds for the numbers of non-zero digits in the $\beta $-expansions of algebraic numbers. As applications, we give criteria for transcendence of the values of power series at certain algebraic points.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 4 , June 2015 , pp. 1243 - 1262
Copyright
© Cambridge University Press, 2014 

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