On univoque Pisot numbers
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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