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ArticleOriginal scientific text

Title

On a problem of Alfréd Rényi

Authors 1, 2, 1

Affiliations

  1. Applied Mathematics, Departament d'Economia i Empresa, Univ. Pompeu Fabra, c/ Ramon Trias Fargas 25-27, 08005 Barcelona, Spain
  2. Facultat de Ciències de l'Educació, Univ. Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

Keywords

ENG
Pierce expansions, Engel's series, metric theory

Bibliography

  1. E. Borel, Sur les développements unitaires normaux, C. R. Acad. Sci. Paris 225 (1947), 773.
  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.
  3. J. Galambos, Representations of Real Numbers by Infinite Series, Lecture Notes in Math. 502, Springer, Berlin, 1976.
  4. J. Galambos, The Asymptotic Theory of Extreme Order Statistics, Wiley, New York, 1978; 2nd ed.: Robert Krieger, Malabar, FL, 1987.
  5. K. Jordan, Calculus of Finite Differences, 3rd ed., Chelsea, New York, 1979. (First ed. Budapest, 1939).
  6. P. Lévy, Remarques sur un théorème de M. Émile Borel, C. R. Acad. Sci. Paris 225 (1947), 918-919.
  7. J. Paradís, Ll. Bibiloni and P. Viader, On actually computable bijections between ℕ and ℚ⁺, Order 13 (1996), 369-377.
  8. J. Paradís, P. Viader and Ll. Bibiloni, Approximation of irrational quadratics and their Pierce expansions, Fibonacci Quart. 36 (1998), 146-153.
  9. A. Rényi, A new approach to the theory of Engel's series, Ann. Univ. Sci. Budapest Sect. Math. 5 (1962), 25-32.
  10. F. Schweiger, Ergodic Theory of Fibred Systems and Metric Number Theory, Clarendon Press, Oxford, 1995.
  11. J. O. Shallit, Some predictable Pierce expansions, Fibonacci Quart. 22 (1984), 332-335.
  12. J. O. Shallit, Metric theory of Pierce expansions, ibid. 24 (1986), 22-40.
  13. J. O. Shallit, Pierce expansions and rules for the determination of leap years, ibid. 32 (1994), 416-423.
  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. D. Williams, On Rényi's 'record' problem and Engel's series, Bull. London Math. Soc. 5 (1973), 235-237.
Acta Arithmetica
1999/91/2
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Pages:
107-115
Main language of publication
English
Received
1998-06-19
Accepted
1999-05-11
Published
1999
Exact and natural sciences