Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
Published electronically: January 10, 2007
MathSciNet review: 2299792
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11R06, 11A67

Retrieve articles in all journals with MSC (2000): 11R06, 11A67

Additional Information

Jean-Paul Allouche
Affiliation: CNRS, LRI, Bâtiment 490, Université Paris-Sud, 91405 Orsay Cedex, France

Christiane Frougny
Affiliation: LIAFA, CNRS UMR 7089, 2 place Jussieu, 75251 Paris Cedex 05, France, and Université Paris 8

Kevin G. Hare
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Keywords: Univoque, Pisot number, beta-expansion
Received by editor(s): June 13, 2006
Received by editor(s) in revised form: August 15, 2006
Published electronically: January 10, 2007
Additional Notes: Research of the first author was partially supported by MENESR, ACI NIM 154 Numération.
Research of the third author was supported, in part, by NSERC of Canada.
Article copyright: © Copyright 2007 American Mathematical Society