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On univoque Pisot numbers

J. -P. Allouche·C. Frougny·K. G. Hare
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Abstract

We study Pisot numbers $\beta \in (1, 2)$ which are univoque, i.e., such that there exists only one representation of 1 as $1 = \sum_{n \geq 1} s_n\beta^{-n}$, 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.

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J. -P. Allouche, C. Frougny, K. G. Hare. 2006-10-23. On univoque Pisot numbers. https://doi.org/10.1090/s0025-5718-07-01961-8

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