On univoque Pisot numbers

Abstract

We study Pisot numbers $\beta \in (1,2)$ which are univoque, i.e., such that there exists only one representation of 1 as $1={\sum }_{n\ge 1}{s}_n{\beta }^{-n}$, with $s_n\in \{0,1\}$. 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.

Accepted by Mathematics of COmputation

Cited by in corpus (1)

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