On the law of the iterated logarithm for the discrepancy of lacunary sequences

DOI10.1090/S0002-9947-2010-05026-3zbMath1209.11072MaRDI QIDQ3056576

Christoph Aistleitner

Publication date: 12 November 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

law of the iterated logarithmlacunary seriesDiscrepancy

Mathematics Subject Classification ID

Strong limit theorems (60F15) Irregularities of distribution, discrepancy (11K38) Lacunary series of trigonometric and other functions; Riesz products (42A55) General theory of distribution modulo (1) (11K06)

Related Items (25)

A metric discrepancy result for lacunary sequences ⋮ Metric discrepancy results for subsequences of geometric progressions ⋮ Metric discrepancy results for geometric progressions with large ratios ⋮ Metric discrepancy results for alternating geometric progressions ⋮ Strong approximation of lacunary series with random gaps ⋮ On the Uniform Theory of Lacunary Series ⋮ Diophantine equations and the LIL for the discrepancy of sublacunary sequences ⋮ On the law of the iterated logarithm for trigonometric series with bounded gaps ⋮ Metric discrepancy results for geometric progressions with large ratios. II ⋮ On the class of limits of lacunary trigonometric series ⋮ Limit distributions in metric discrepancy theory ⋮ Metric discrepancy results for geometric progressions perturbed by irrational rotations ⋮ A metric discrepancy result for the sequence of powers of minus two ⋮ Quantitative uniform distribution results for geometric progressions ⋮ Metric discrepancy results for subsequences of \(\{\theta^k x\}\) ⋮ On the maximal spectral type of a class of rank one transformations ⋮ A metric discrepancy result with given speed ⋮ Irregular discrepancy behavior of lacunary series ⋮ Irregular discrepancy behavior of lacunary series. II ⋮ The central limit theorem for complex Riesz-Raikov sums ⋮ The law of the iterated logarithm for the discrepancy of perturbed geometric progressions ⋮ On the law of the iterated logarithm for permuted lacunary sequences ⋮ PROBABILITY AND METRIC DISCREPANCY THEORY ⋮ On the law of the iterated logarithm for the discrepancy of lacunary sequences II ⋮ Extremal discrepancy behavior of lacunary sequences

Cites Work

• On the central limit theorem for \(f(n_{k}x)\)
• The law of the iterated logarithm for discrepancies of \(\{\theta^{n}x\}\)
• On the distribution of values of sums of the type \(\sum f(2^kt)\)
• Metric Number Theory and the Large Sieve
• An A.S. Invariance principle for lacunary seriesf(n k x)
• On the asymptotic behaviour of ?f(nkx)
• The Size of Trigonometric and Walsh Series and Uniform Distribution Mod 1
• The discrepancy of random sequences {kx}
• Limit theorems for lacunary series and uniform distribution mod 1
• An asymptotic property of a gap sequence
• Probability methods in some problems of analysis and number theory
• On the central limit theorem for lacunary trigonometric series
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