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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
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.
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- © Cambridge University Press, 2014
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