On a problem of Alfréd Rényi

Pelegrí Viader; Lluís Bibiloni; Jaume Paradís

Acta Arithmetica (1999)

  • Volume: 91, Issue: 2, page 107-115
  • ISSN: 0065-1036

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Pelegrí Viader, Lluís Bibiloni, and Jaume Paradís. "On a problem of Alfréd Rényi." Acta Arithmetica 91.2 (1999): 107-115. <http://eudml.org/doc/207342>.

@article{PelegríViader1999,
author = {Pelegrí Viader, Lluís Bibiloni, Jaume Paradís},
journal = {Acta Arithmetica},
keywords = {Pierce expansions; Engel's series; metric theory; irrational number},
language = {eng},
number = {2},
pages = {107-115},
title = {On a problem of Alfréd Rényi},
url = {http://eudml.org/doc/207342},
volume = {91},
year = {1999},
}

TY - JOUR
AU - Pelegrí Viader
AU - Lluís Bibiloni
AU - Jaume Paradís
TI - On a problem of Alfréd Rényi
JO - Acta Arithmetica
PY - 1999
VL - 91
IS - 2
SP - 107
EP - 115
LA - eng
KW - Pierce expansions; Engel's series; metric theory; irrational number
UR - http://eudml.org/doc/207342
ER -

References

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  1. [1] E. Borel, Sur les développements unitaires normaux, C. R. Acad. Sci. Paris 225 (1947), 773. Zbl0029.15303
  2. [2] P. Erdős, A. Rényi and P. Szüsz, On Engel's and Sylvester's series, Ann. Univ. Sci. Budapest. Sect. Math. 1 (1958), 7-32. Zbl0107.27002
  3. [3] J. Galambos, Representations of Real Numbers by Infinite Series, Lecture Notes in Math. 502, Springer, Berlin, 1976. Zbl0322.10002
  4. [4] J. Galambos, The Asymptotic Theory of Extreme Order Statistics, Wiley, New York, 1978; 2nd ed.: Robert Krieger, Malabar, FL, 1987. Zbl0381.62039
  5. [5] K. Jordan, Calculus of Finite Differences, 3rd ed., Chelsea, New York, 1979. (First ed. Budapest, 1939). Zbl0060.12309
  6. [6] P. Lévy, Remarques sur un théorème de M. Émile Borel, C. R. Acad. Sci. Paris 225 (1947), 918-919. 
  7. [7] J. Paradís, Ll. Bibiloni and P. Viader, On actually computable bijections between ℕ and ℚ⁺, Order 13 (1996), 369-377. Zbl0941.11004
  8. [8] J. Paradís, P. Viader and Ll. Bibiloni, Approximation of irrational quadratics and their Pierce expansions, Fibonacci Quart. 36 (1998), 146-153. Zbl0911.11007
  9. [9] A. Rényi, A new approach to the theory of Engel's series, Ann. Univ. Sci. Budapest Sect. Math. 5 (1962), 25-32. Zbl0232.10028
  10. [10] F. Schweiger, Ergodic Theory of Fibred Systems and Metric Number Theory, Clarendon Press, Oxford, 1995. Zbl0819.11027
  11. [11] J. O. Shallit, Some predictable Pierce expansions, Fibonacci Quart. 22 (1984), 332-335. Zbl0546.10005
  12. [12] J. O. Shallit, Metric theory of Pierce expansions, ibid. 24 (1986), 22-40. Zbl0598.10057
  13. [13] J. O. Shallit, Pierce expansions and rules for the determination of leap years, ibid. 32 (1994), 416-423. Zbl0823.11043
  14. [14] W. Sierpiński, Sur quelques algorithmes pour développer les nombres réels en série, C. R. Soc. Sci. Varsovie 4 (1911), 56-77 (in Polish). A French translation can be found in Oeuvres choisies, T. I, Varsovie, 1974, 236-254. 
  15. [15] D. Williams, On Rényi's 'record' problem and Engel's series, Bull. London Math. Soc. 5 (1973), 235-237. Zbl0292.60047

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