Cyclic shifts of the van der corput set

Dmitriy Bilyk

doi:10.1090/S0002-9939-09-09854-2

Cyclic shifts of the van der corput set

Dmitriy Bilyk

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In 1980, K. Roth showed that the expected value of the L² discrepancy of the cyclic shifts of the N-point van der Corput set is bounded by a constant multiple of logN, thus guaranteeing the existence of a shift with asymptotically minimal L² discrepancy. In the present paper, we construct a specific example of such a shift.

Original language	English (US)
Pages (from-to)	2591-2600
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	137
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9939-09-09854-2
State	Published - Aug 2009
Externally published	Yes

Keywords

Discrepancy theory
Fourier analysis

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10.1090/S0002-9939-09-09854-2

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title = "Cyclic shifts of the van der corput set",

abstract = "In 1980, K. Roth showed that the expected value of the L2 discrepancy of the cyclic shifts of the N-point van der Corput set is bounded by a constant multiple of logN, thus guaranteeing the existence of a shift with asymptotically minimal L2 discrepancy. In the present paper, we construct a specific example of such a shift.",

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author = "Dmitriy Bilyk",

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AU - Bilyk, Dmitriy

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N2 - In 1980, K. Roth showed that the expected value of the L2 discrepancy of the cyclic shifts of the N-point van der Corput set is bounded by a constant multiple of logN, thus guaranteeing the existence of a shift with asymptotically minimal L2 discrepancy. In the present paper, we construct a specific example of such a shift.

AB - In 1980, K. Roth showed that the expected value of the L2 discrepancy of the cyclic shifts of the N-point van der Corput set is bounded by a constant multiple of logN, thus guaranteeing the existence of a shift with asymptotically minimal L2 discrepancy. In the present paper, we construct a specific example of such a shift.

KW - Discrepancy theory

KW - Fourier analysis

UR - https://www.scopus.com/pages/publications/77951080765

UR - https://www.scopus.com/pages/publications/77951080765#tab=citedBy

U2 - 10.1090/S0002-9939-09-09854-2

DO - 10.1090/S0002-9939-09-09854-2

M3 - Article

AN - SCOPUS:77951080765

SN - 0002-9939

VL - 137

SP - 2591

EP - 2600

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 8

ER -

Cyclic shifts of the van der corput set

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