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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: 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.


References [Enhancements On Off] (What's this?)

  • [1] G. H. Hardy, J. E. Littlewood and G. Pó1ya, Inequalities, Cambridge Univ. Press, New York, 1934. MR 13, 727.
  • [2] K. F. Roth, On irregularities of distribution, Mathematika 1 (1954), 73-79. MR 16, 575. MR 0066435 (16:575c)
  • [3] W. M. Schmidt, Irregularities of distribution. II, Trans. Amer. Math. Soc. 136 (1969), 347-360. MR 38 #3237. MR 0234923 (38:3237)
  • [4] -, Irregularities of distribution. III, Pacific J. Math. 29 (1969), 225-234. MR 0245531 (39:6837)
  • [5] -, Irregularities of distribution. IV, Invent. Math. 7 (1969), 55-82. MR 0245532 (39:6838)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0263748-9
Keywords: Uniform distribution, irregularities of distribution, points on a sphere
Article copyright: © Copyright 1970 American Mathematical Society

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