Cyclic shifts of the van der Corput set
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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.References
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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