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Cyclic shifts of the van der Corput set

Author: Dmitriy Bilyk
Journal: Proc. Amer. Math. Soc. 137 (2009), 2591-2600
MSC (2000): Primary 11K38; Secondary 42B05
Published electronically: March 3, 2009
MathSciNet review: 2497470
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Abstract: In 1980, K. Roth showed that the expected value of the $ L^2$ discrepancy of the cyclic shifts of the $ N$-point van der Corput set is bounded by a constant multiple of $ \sqrt{\log N}$, thus guaranteeing the existence of a shift with asymptotically minimal $ L^2$ discrepancy. In the present paper, we construct a specific example of such a shift.

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Additional Information

Dmitriy Bilyk
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Caro- lina 29208
Address at time of publication: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540

Keywords: Discrepancy theory, Fourier analysis
Received by editor(s): October 22, 2008
Published electronically: March 3, 2009
Additional Notes: The author is grateful to the Fields Institute and the Institute for Advanced Study for hospitality and to the National Science Foundation for support (grants DMS-0801036 and DMS-0635607).
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.