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

DOI:
https://doi.org/10.1090/S0002-9939-2011-10940-7

Published electronically:
June 23, 2011

MathSciNet review:
2869060

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that every value greater than or equal to 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:
https://doi.org/10.1090/S0002-9939-2011-10940-7

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.