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Monatshefte für Mathematik

, Volume 72, Issue 3, pp 264–269 | Cite as

Good lattice points in the sense of Hlawka and Monte-Carlo integration

  • S. K. Zaremba
Article

Keywords

Lattice Point Good Lattice Good Lattice Point 
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References

  1. [1]
    J. C. van der Corput: Verteilungsfunktionen, Proc. Ned. Akad. van Wet., vol.38, pp. 1058–1066 (1935).Google Scholar
  2. [2]
    H. Hancock: Development of the Minkowski Geometry of Numbers, MacMillan, New York, 1939. (Reprinted by Dover, New York, 1964).Google Scholar
  3. [3]
    E. Hlawka: Funktionen von beschränkter Variation in der Theorie der Gleichverteilung, Ann. Mat. Pura. App. (iv), vol.54, pp. 325 (1961).Google Scholar
  4. [4]
    E. Hlawka: Zur angenäherten Berechnung mehrfacher Integrale, Monatsh. Math., vol.66, pp. 140–151 (1962).Google Scholar
  5. [5]
    J. F. Koksma: A general theorem from the theory of uniform distribution modulo 1, Mathematica Zutphen B, vol.11, pp. 7–11 (1942) [Dutch; quoted after Mathematical Reviews].Google Scholar
  6. [6]
    K. F. Roth: On irregularities of distribution, Mathematika, vol.1, pp. 73–79 (1954).Google Scholar
  7. [7]
    S. K. Zaremba: Good lattice points, discrepancy and numerical integration, Ann. Mat. Pura Appl. (iv), vol.73, pp. 293–317 (1966).Google Scholar

Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • S. K. Zaremba
    • 1
  1. 1.MadisonUSA

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