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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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On univoque Pisot numbers
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by Jean-Paul Allouche, Christiane Frougny and Kevin G. Hare PDF
Math. Comp. 76 (2007), 1639-1660 Request permission


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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Additional Information
  • Jean-Paul Allouche
  • Affiliation: CNRS, LRI, Bâtiment 490, Université Paris-Sud, 91405 Orsay Cedex, France
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  • Christiane Frougny
  • Affiliation: LIAFA, CNRS UMR 7089, 2 place Jussieu, 75251 Paris Cedex 05, France, and Université Paris 8
  • Email:
  • Kevin G. Hare
  • Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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  • 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.
  • © Copyright 2007 American Mathematical Society
  • Journal: Math. Comp. 76 (2007), 1639-1660
  • MSC (2000): Primary 11R06; Secondary 11A67
  • DOI:
  • MathSciNet review: 2299792