The Khinchin inequality and Chen's theorem

-discrepancies is one of the basic results in the theory of uniformly distributed point sets. This is a difficult result, based on deep and nontrivial combinatorial arguments (see the papers by Chen and Beck on irregularities of distributions). The paper is aimed at showing that the results of such...

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Bibliographic Details
Published in:St. Petersburg mathematical journal 2012-08, Vol.23 (4), p.761-778
Main Author: Skriganov, M. M.
Format: Article
Language:English
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Summary:-discrepancies is one of the basic results in the theory of uniformly distributed point sets. This is a difficult result, based on deep and nontrivial combinatorial arguments (see the papers by Chen and Beck on irregularities of distributions). The paper is aimed at showing that the results of such a type are intimately related to lacunarity and statistical independence of certain function series. In particular, the classical Khinchin inequality for the Rademacher functions is employed to prove an important generalization of Chen's theorem. In a forthcoming paper, the author will continue the study of the phenomena of lacunarity and statistical independence in the context of the theory of uniformly distributed point sets.]]>
ISSN:1061-0022
1547-7371
DOI:10.1090/S1061-0022-2012-01216-1