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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Cyclic shifts of the van der Corput set
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by Dmitriy Bilyk PDF
Proc. Amer. Math. Soc. 137 (2009), 2591-2600 Request permission

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
  • MR Author ID: 757936
  • Email: bilyk@math.ias.edu
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 2591-2600
  • MSC (2000): Primary 11K38; Secondary 42B05
  • DOI: https://doi.org/10.1090/S0002-9939-09-09854-2
  • MathSciNet review: 2497470