Limit theorems for lacunary series and uniform distribution mod 1

DOI10.4064/aa-26-3-241-251zbMath0263.10020OpenAlexW880608189MaRDI QIDQ5678928

Walter Philipp

Publication date: 1975

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/205312

Mathematics Subject Classification ID

Lacunary series of trigonometric and other functions; Riesz products (42A55) General theory of distribution modulo (1) (11K06)

Related Items

A metric discrepancy result for lacunary sequences, Metric discrepancy results for subsequences of geometric progressions, Large deviation principles for lacunary sums, Metric discrepancy results for geometric progressions with large ratios, On the law of the iterated logarithm for trigonometric series with bounded gaps. II, Metric discrepancy results for alternating geometric progressions, On the central limit theorem for \(f(n_{k}x)\), On sequences with prescribed metric discrepancy behavior, Metric discrepancy results for geometric progressions with small ratios, 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, On evil Kronecker sequences and lacunary trigonometric products, 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, A metric discrepancy result for a lacunary sequence with small gaps, Metric discrepancy results for geometric progressions perturbed by irrational rotations, Normal Numbers and Computer Science, Some theorems on metric uniform distribution using \(L^ 2\) methods, Zur Diskrepanz bezüglich gewichteter Mittel, Metric Discrepancy Results for Sequences {nkx} and Diophantine Equations, Covering numbers, dyadic chaining and discrepancy, A metric discrepancy result for the sequence of powers of minus two, Fractal Dimensions and Random Transformations, Quantitative uniform distribution results for geometric progressions, Metric discrepancy results for subsequences of \(\{\theta^k x\}\), On the convergence of ∑𝑐_{𝑛}𝑓(𝑛𝑥) and the Lip 1/2 class, On the discrepancy of Markov-normal sequences, The law of the iterated logarithm for discrepancies of \(\{\theta^{n}x\}\), A metric discrepancy result with given speed, Obituary for Walter Philipp., A metric discrepancy result for the Hardy-Littlewood-Pólya sequences, Irregular discrepancy behavior of lacunary series, A law of the iterated logarithm for discrepancies: non-constant limsup, Irregular discrepancy behavior of lacunary series. II, Normal numbers and nested perfect necklaces, On the law of the iterated logarithm for the discrepancy of lacunary sequences, Empirical Distribution Functions and Strong Approximation Theorems for Dependent Random Variables. A Problem of Baker in Probabilistic Number Theory, The law of the iterated logarithm for the discrepancy of perturbed geometric progressions, On the law of the iterated logarithm for permuted lacunary sequences, Geometric and measure-theoretic shrinking targets in dynamical systems, On the asymptotic behaviour of ?f(nkx), On the asymptotic behaviour of ?f(nkx), On the law of the iterated logarithm for the discrepancy of lacunary sequences II, The law of the iterated logarithm for the discrepancies of a permutation of \(\{n_kx\}\), Extremal discrepancy behavior of lacunary sequences