Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11K38, 42B05

Retrieve articles in all journals with MSC (2000): 11K38, 42B05


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
Email: bilyk@math.ias.edu

DOI: http://dx.doi.org/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
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.