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Slice discrepancy and irregularities of distribution on spheres
Author(s) -
Blümlinger Martin
Publication year - 1991
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300006483
Subject(s) - spheres , mathematics , intersection (aeronautics) , logarithm , distribution (mathematics) , point (geometry) , combinatorics , upper and lower bounds , mathematical analysis , geometry , physics , astronomy , engineering , aerospace engineering
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.