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On irregularities of distribution III

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  09 April 2009

W. W. L. Chen
W. W. L. Chen
Affiliation:
School of MPCEMacquarie UniversitySydney NSW 2109Australia e-mail: wchen@mpce.mq.edu.au
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Abstract

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We study the Lw-norm (2 ≤ W < ∞) of the discrepancy of a sequence of points in the unit cube relative to similar copies of a given convex polygon. In particular, we prove the rather surprising result that the estimates obtained have the same order of magnitude as the analogous question when the sequence of points is replaced by a set of points.

MSC classification

Secondary: 11K38: Irregularities of distribution, discrepancy
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 2 , April 1996 , pp. 228 - 244
Copyright
Copyright © Australian Mathematical Society 1996

References

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