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. Jean-Paul Allouche, A note on univoque self-Sturmian numbers
  7. Tomáš Hejda, Zuzana Masáková, Edita Pelantová, Greedy and lazy representations in negative base systems
  8. Takao Komatsu, An approximation property of quadratic irrationals

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