On univoque Pisot numbers

Details On univoque Pisot numbers On univoque Pisot numbers

2006-10-23

arxiv.org/abs/math/0610681v1

Math. Comp. 76 (2007) 1639-1660

Mathematics

Number Theory

Accepted by Mathematics of COmputation

Scientific paper

10.1090/S0025-5718-07-01961-8

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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