Empirical processes in probabilistic number theory: the LIL for the discrepancy of \((n_{k}\omega)\bmod 1\)

zbMath1145.11058MaRDI QIDQ2505467

István Berkes, Robert F. Tichy, Walter Philipp

Publication date: 26 September 2006

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

discrepancyDiophantine equationKolmogorov-Smirnov statisticlow of the iterated logarithmsub-Hadamard growth condition

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Strong limit theorems (60F15) Counting solutions of Diophantine equations (11D45) Irregularities of distribution, discrepancy (11K38)

Related Items (11)

Metric discrepancy results for alternating geometric progressions ⋮ Diophantine equations and the LIL for the discrepancy of sublacunary sequences ⋮ On the limit distribution of the well-distribution measure of random binary sequences ⋮ On the class of limits of lacunary trigonometric series ⋮ A metric discrepancy result for a lacunary sequence with small gaps ⋮ A metric discrepancy result for the sequence of powers of minus two ⋮ Quantitative uniform distribution results for geometric progressions ⋮ Pseudorandom numbers and entropy conditions ⋮ A metric discrepancy result for the Hardy-Littlewood-Pólya sequences ⋮ A law of the iterated logarithm for discrepancies: non-constant limsup ⋮ On the asymptotic behavior of weakly lacunary series

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