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On univoque Pisot numbers

J. -P. Allouche, C. Frougny, K. G. Hare

math.NTarXiv:math/0610681

Abstract

We study Pisot numbers β∈ (1, 2) which are univoque, i.e., such that there exists only one representation of 1 as 1 = Σn ≥ 1 snβ-n, with sn ∈ \0, 1\. We prove in particular that there exists a smallest univoque Pisot number, which has degree 14. Furthermore we give the smallest limit point of the set of univoque Pisot numbers.

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