Irregularities of distribution. V
Author:
Wolfgang M. Schmidt
Journal:
Proc. Amer. Math. Soc. 25 (1970), 608-614
MSC:
Primary 10.33
DOI:
https://doi.org/10.1090/S0002-9939-1970-0263748-9
MathSciNet review:
0263748
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Abstract | References | Similar Articles | Additional Information
Abstract: It is shown that for any finite or countable number of points with positive weights on the sphere, there is always a spherical cap such that the sum of the weights of the points in the cap is rather different from the expected value.
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G. H. Hardy, J. E. Littlewood and G. Pó1ya, Inequalities, Cambridge Univ. Press, New York, 1934. MR 13, 727.
- K. F. Roth, On irregularities of distribution, Mathematika 1 (1954), 73–79. MR 66435, DOI https://doi.org/10.1112/S0025579300000541
- Wolfgang M. Schmidt, Irregularities of distribution. II, Trans. Amer. Math. Soc. 136 (1969), 347–360. MR 234923, DOI https://doi.org/10.1090/S0002-9947-1969-0234923-0
- Wolfgang M. Schmidt, Irregularities of distribution. III, Pacific J. Math. 29 (1969), 225–234. MR 245531
- Wolfgang M. Schmidt, Irregularities of distribution. IV, Invent. Math. 7 (1969), 55–82. MR 245532, DOI https://doi.org/10.1007/BF01418774
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Additional Information
Keywords:
Uniform distribution,
irregularities of distribution,
points on a sphere
Article copyright:
© Copyright 1970
American Mathematical Society