On univoque Pisot numbers

J. -P. Allouche; C. Frougny; K. G. Hare

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

On univoque Pisot numbers

Number Theory 2009-11-11 v1

Authors: J. -P. Allouche , C. Frougny , K. G. Hare

View on arXiv ↗ PDF ↗ DOI ↗

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.

Cite

@article{arxiv.math/0610681,
  title  = {On univoque Pisot numbers},
  author = {J. -P. Allouche and C. Frougny and K. G. Hare},
  journal= {arXiv preprint arXiv:math/0610681},
  year   = {2009}
}

Comments

Accepted by Mathematics of COmputation

Related papers

View all related →