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Slice discrepancy and irregularities of distribution on spheres

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

Published online by Cambridge University Press:  26 February 2010

Martin Blümlinger
Martin Blümlinger
Affiliation:
Dr. M. Blümlinger, Institut für Analysis, Technische Mathematik und Versicherungsmathematik, Technische Universität Wien, Austria.
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Abstract

We improve W. Schmidt's lower bound for the slice (intersection of two halfspheres) discrepancy of point distributions on spheres and show that this estimate is up to a logarithmic factor best possible. It is shown that the slice and spherical cap discrepancies are equivalent for the definition of uniformly distributed sequences on spheres.

MSC classification

Secondary: 11K38: Irregularities of distribution, discrepancy
Type
Research Article
Information
Mathematika , Volume 38 , Issue 1 , June 1991 , pp. 105 - 116
Copyright
Copyright © University College London 1991

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