Characterization of the unique expansions 1 = ∑ i = 1 ∞ q - n i and related problems

Pál Erdös; Istvá n Joó; Vilmos Komornik

Bulletin de la Société Mathématique de France (1990)

  • Volume: 118, Issue: 3, page 377-390
  • ISSN: 0037-9484

How to cite

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Erdös, Pál, Joó, Istvá n, and Komornik, Vilmos. "Characterization of the unique expansions $1=\sum ^{\infty }_{i=1}q^{-n_ i}$ and related problems." Bulletin de la Société Mathématique de France 118.3 (1990): 377-390. <http://eudml.org/doc/87609>.

@article{Erdös1990,
author = {Erdös, Pál, Joó, Istvá n, Komornik, Vilmos},
journal = {Bulletin de la Société Mathématique de France},
keywords = {nonintegral base; uniqueness; number of consecutive zero digits; greedy expansion; real numbers},
language = {eng},
number = {3},
pages = {377-390},
publisher = {Société mathématique de France},
title = {Characterization of the unique expansions $1=\sum ^\{\infty \}_\{i=1\}q^\{-n_ i\}$ and related problems},
url = {http://eudml.org/doc/87609},
volume = {118},
year = {1990},
}

TY - JOUR
AU - Erdös, Pál
AU - Joó, Istvá n
AU - Komornik, Vilmos
TI - Characterization of the unique expansions $1=\sum ^{\infty }_{i=1}q^{-n_ i}$ and related problems
JO - Bulletin de la Société Mathématique de France
PY - 1990
PB - Société mathématique de France
VL - 118
IS - 3
SP - 377
EP - 390
LA - eng
KW - nonintegral base; uniqueness; number of consecutive zero digits; greedy expansion; real numbers
UR - http://eudml.org/doc/87609
ER -

References

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  1. [1] RÉNYI (A.). — Representations for real numbers and their ergodic properties, Acta Math. Hungar., t. 8, 1957, p. 477-493. Zbl0079.08901MR20 #3843
  2. [2] PARRY (W.). — On the β-expansions of real numbers, Acta Math. Hungar., t. 11, 1960, p. 401-416. Zbl0099.28103MR26 #288
  3. [3] BERTRAND (A.). — Développements en base de Pisot et répartition modulo 1 de la suite ({x΋n}), Thèse de 3ème cycle, Université de Bordeaux I, n° 1595, 1981. 
  4. [4] ERDÖS (P.) and JOÓ (I.). — On the expansions 1 = Σq-ni, 1 &lt; q &lt; 2, to appear. 
  5. [5] ERDÖS (P.), HORVÁTH (M.) and JOÓ (I.). — On the uniqueness of the expansions 1 = Σq-ni, to appear. 
  6. [6] JOÓ (I.). — On the distribution of the set {ΣNi=1 εiqi : εi = 0,1}, to appear. Zbl0766.11005
  7. [7] JOÓ (I.) and JOÓ (M.). — On an arithmetical property of √2, to appear. 
  8. [8] BOGMÉR (A.), HORVÁTH (M.) and SÖVEGJÁRTÓ (A.). — On some problems of I. JOÓ, to appear. Zbl0766.11004
  9. [9] RAUZY (G.). — Sur les développements en base non entière, [Colloque de Théorie des nombres, Alger], 21-23 octobre 1989, to appear. 

Citations in EuDML Documents

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  1. P. Erdös, M. Joó, I. Joó, On a problem of Tamas Varga
  2. Jean-Paul Allouche, A note on univoque self-sturmian numbers
  3. Paul Erdős, István Joó, Vilmos Komornik, On the sequence of numbers of the form ε ₀ + ε ₁ q + . . . + ε n q n , ε i ∈ 0 , 1
  4. Toufik Zaïmi, On an approximation property of Pisot numbers II
  5. Toufik Zaimi, Commentaires sur quelques résultats sur les nombres de Pisot
  6. Tomáš Hejda, Zuzana Masáková, Edita Pelantová, Greedy and lazy representations in negative base systems
  7. Jean-Paul Allouche, A note on univoque self-Sturmian numbers
  8. Takao Komatsu, An approximation property of quadratic irrationals

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