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On infinite series representations of real numbers. (English) Zbl 0274.10011


MSC:

11A63 Radix representation; digital problems
11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
11K60 Diophantine approximation in probabilistic number theory
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References:

[1] J. Galambos : The ergodic properties of the denominators in the Oppenheim expansion of real numbers into infinite series of rationals . Quart. J. Math. Oxford Ser., 21 (1970) 177-191. · Zbl 0198.38104
[2] J. Galambos : A generalization of a theorem of Borel concerning the distribution of digits in dyadic expansions . Amer. Math. Monthly, 78 (1971) 774-779. · Zbl 0238.10038
[3] J. Galambos : On a model for a fair distribution of gifts . J. Appl. Probability, 8 (1971) 681-690. · Zbl 0227.60007
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[5] J. Galambos : Probabilistic theorems concerning expansions of real numbers . Periodica Math. Hungar., 3 (1973) 101-113. · Zbl 0247.10032
[6] J. Galambos : Further ergodic results on the Oppenheim series . Quart. J. Math. Oxford Ser., 25 (1974) (to appear). · Zbl 0281.10028
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[8] A. Oppenheim : Representations of real numbers by series of reciprocals of odd integers . Acta Arith., 18 (1971) 115-124. · Zbl 0237.10011
[9] A. Oppenheim : The representation of real numbers by infinite series of rationals . Acta Arith., 21 (1972) 391-398. · Zbl 0258.10003
[10] T. Salát : Zur metrische Theorie der Lürothschen Entwicklungen der reellen Zahlen . Czechosl. Math. J., 18 (1968) 489-522. · Zbl 0162.34703
[11] F. Schweiger : Metrische Sätze über Oppenheimentwicklungen . J. Reine Angew. Math., 254 (1972) 152-159. · Zbl 0234.10040
[12] W. Vervaat : Success epochs in Bernoulli trials with applications in number theory . Math. Centre Tracts, Vol. 42, (1972) Amsterdam. · Zbl 0267.60003
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