Studia Scientiarium Mathematicarum Hungarica 31. (1996)

1-3. szám - Berkes I.-Philipp W.: Trigonometric series and uniform distribution mod 1

TRIGONOMETRIC SERIES AND UNIFORM DISTRIBUTION MOD 1 25 [17] Kuipers, L. and Niederreiter, H., Uniform distribution of sequences, Pure and Ap­plied Mathematics, Wiley, New York-London-Sydney, 1974. MR 54 #7415 [18] Philipp, W., Limit theorems for lacunary series and uniform distribution mod 1, Acta A nth. 26 (1974/75), 241-251. MR 52 #325 [19] Philipp, W., A functional law of the iterated logarithm for empirical distribution functions of weakly dependent random variables, Ann. Probab. 5 (1977), 319-350. MR 56 #1397 [20] Philipp, W., Empirical distribution functions and strong approximation theorems for dependent random variables. A problem of Baker in probabilistic number theory, Trans. Amer. Math. Soc. 345 (1994), 707-727. [21] Philipp, W. and Stout, W., Almost sure invariance principles for partial sums of weakly dependent random variables, Mem. Amer. Math. Soc. 2 (1975), issue 2, no. 161, 1975. MR 55 #6570 [22] Révész, P., The laws of large numbers, Probability and Mathematical Statistics, Vol. 4, Academic Press, New York-London, 1968. MR 39 #6391 [23] Salem, R. and Zygmund, A., On lacunary trigonometric series, Proc. Nat. Acad. Set. U.S.A. 33 (1947), 333-338. MR 9-181 [24] Salem, R. and Zygmund, A., La lói du logarithme itéré pour les series trigonométriques lacunaires, Bull. Set. Math. (2) 74 (1950), 209-224. MR 12-605 [25] Takahashi, S., On the law of the iterated logarithm for lacunary trigonometric series, Tóhoku Math. J. (2) 24 (1972), 319-329. Zbl 241.42007 [26] Takahashi, S., On the law of the iterated logarithm for lacunary trigonometric series II, Tóhoku Math. J. (2) 27 (1975), 391-403. Zbl 315.40009 [27] Tijdeman, R., On integers with many small prime factors, Compositio Math. 26 (1973), 319-330. MR 48 #3896 [28] Weyl, H., Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352. Jb. Fortschritte Math. 46, 278-280 (Received February 23, 1995) MTA MATEMATIKAI KUTATÓINTÉZETE POSTAFIÓK 127 H—1364 BUDAPEST HUNGARY DEPARTMENT OF STATISTICS UNIVERSITY OF ILLINOIS 725 S. WRIGHT STREET CHAMPAIGN, IL 61820 U.S.A.

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