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Cyclic shifts of the van der Corput set
Author(s):
Dmitriy
Bilyk
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2591-2600.
MSC (2000):
Primary 11K38;
Secondary 42B05
Posted:
March 3, 2009
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Abstract:
In 1980, K. Roth showed that the expected value of the  discrepancy of the cyclic shifts of the  -point van der Corput set is bounded by a constant multiple of  , thus guaranteeing the existence of a shift with asymptotically minimal  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 Carolina 29208
Address at time of publication:
School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
Email:
bilyk@math.ias.edu
DOI:
10.1090/S0002-9939-09-09854-2
PII:
S 0002-9939(09)09854-2
Keywords:
Discrepancy theory,
Fourier analysis
Received by editor(s):
October 22, 2008
Posted:
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 of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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