On a problem of Alfréd Rényi
Pelegrí Viader ; Lluís Bibiloni ; Jaume Paradís
Acta Arithmetica, Tome 89 (1999), p. 107-115 / Harvested from The Polish Digital Mathematics Library
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Publié le : 1999-01-01
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     title = {On a problem of Alfr\'ed R\'enyi},
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     volume = {89},
     year = {1999},
     pages = {107-115},
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Pelegrí Viader; Lluís Bibiloni; Jaume Paradís. On a problem of Alfréd Rényi. Acta Arithmetica, Tome 89 (1999) pp. 107-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav91i2p107bwm/

[000] [1] E. Borel, Sur les développements unitaires normaux, C. R. Acad. Sci. Paris 225 (1947), 773. | Zbl 0029.15303

[001] [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. | Zbl 0107.27002

[002] [3] J. Galambos, Representations of Real Numbers by Infinite Series, Lecture Notes in Math. 502, Springer, Berlin, 1976. | Zbl 0322.10002

[003] [4] J. Galambos, The Asymptotic Theory of Extreme Order Statistics, Wiley, New York, 1978; 2nd ed.: Robert Krieger, Malabar, FL, 1987. | Zbl 0381.62039

[004] [5] K. Jordan, Calculus of Finite Differences, 3rd ed., Chelsea, New York, 1979. (First ed. Budapest, 1939). | Zbl 0060.12309

[005] [6] P. Lévy, Remarques sur un théorème de M. Émile Borel, C. R. Acad. Sci. Paris 225 (1947), 918-919.

[006] [7] J. Paradís, Ll. Bibiloni and P. Viader, On actually computable bijections between ℕ and ℚ⁺, Order 13 (1996), 369-377. | Zbl 0941.11004

[007] [8] J. Paradís, P. Viader and Ll. Bibiloni, Approximation of irrational quadratics and their Pierce expansions, Fibonacci Quart. 36 (1998), 146-153. | Zbl 0911.11007

[008] [9] A. Rényi, A new approach to the theory of Engel's series, Ann. Univ. Sci. Budapest Sect. Math. 5 (1962), 25-32. | Zbl 0232.10028

[009] [10] F. Schweiger, Ergodic Theory of Fibred Systems and Metric Number Theory, Clarendon Press, Oxford, 1995. | Zbl 0819.11027

[010] [11] J. O. Shallit, Some predictable Pierce expansions, Fibonacci Quart. 22 (1984), 332-335. | Zbl 0546.10005

[011] [12] J. O. Shallit, Metric theory of Pierce expansions, ibid. 24 (1986), 22-40. | Zbl 0598.10057

[012] [13] J. O. Shallit, Pierce expansions and rules for the determination of leap years, ibid. 32 (1994), 416-423. | Zbl 0823.11043

[013] [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.

[014] [15] D. Williams, On Rényi's 'record' problem and Engel's series, Bull. London Math. Soc. 5 (1973), 235-237. | Zbl 0292.60047