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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A metric discrepancy result for lacunary sequences


Authors: Katusi Fukuyama and Tetsujin Watada
Journal: Proc. Amer. Math. Soc. 140 (2012), 749-754
MSC (2010): Primary 11K38; Secondary 60F15
Published electronically: June 23, 2011
MathSciNet review: 2869060
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Abstract: We prove that every value greater than or equal to $ 1/2 $ can be a constant appearing in the law of the iterated logarithm for discrepancies of a lacunary sequence satisfying the Hadamard gap condition.


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Additional Information

Katusi Fukuyama
Affiliation: Department of Mathematics, Kobe University, Rokko, Kobe, 657-8501 Japan
Email: fukuyama@math.kobe-u.ac.jp

Tetsujin Watada
Affiliation: Department of Mathematics, Kobe University, Rokko, Kobe, 657-8501 Japan

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10940-7
PII: S 0002-9939(2011)10940-7
Keywords: Discrepancy, lacunary sequence, law of the iterated logarithm
Received by editor(s): November 26, 2010
Received by editor(s) in revised form: December 8, 2010
Published electronically: June 23, 2011
Additional Notes: The first author was supported in part by KAKENHI 19204008.
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.