On univoque Pisot numbers

Allouche, Jean-Paul; Frougny, Christiane; Hare, Kevin

doi:10.1090/S0025-5718-07-01961-8

On univoque Pisot numbers

Authors: Jean-Paul Allouche, Christiane Frougny and Kevin G. Hare
Journal: Math. Comp. 76 (2007), 1639-1660
MSC (2000): Primary 11R06; Secondary 11A67
DOI: https://doi.org/10.1090/S0025-5718-07-01961-8
Published electronically: January 10, 2007
MathSciNet review: 2299792
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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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