A two-dimensional van Aardenne-Ehrenfest theorem in irregularities of distribution

József Beck

Compositio Mathematica (1989)

  • Volume: 72, Issue: 3, page 269-339
  • ISSN: 0010-437X

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Beck, József. "A two-dimensional van Aardenne-Ehrenfest theorem in irregularities of distribution." Compositio Mathematica 72.3 (1989): 269-339. <http://eudml.org/doc/89992>.

@article{Beck1989,
author = {Beck, József},
journal = {Compositio Mathematica},
keywords = {irregularities of distribution; discrepancy; k-dimensional unit-cube},
language = {eng},
number = {3},
pages = {269-339},
publisher = {Kluwer Academic Publishers},
title = {A two-dimensional van Aardenne-Ehrenfest theorem in irregularities of distribution},
url = {http://eudml.org/doc/89992},
volume = {72},
year = {1989},
}

TY - JOUR
AU - Beck, József
TI - A two-dimensional van Aardenne-Ehrenfest theorem in irregularities of distribution
JO - Compositio Mathematica
PY - 1989
PB - Kluwer Academic Publishers
VL - 72
IS - 3
SP - 269
EP - 339
LA - eng
KW - irregularities of distribution; discrepancy; k-dimensional unit-cube
UR - http://eudml.org/doc/89992
ER -

References

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  1. 1 Aardenne-Ehrenfest, T. van: "Proof of the impossibility of a just distribution of an infinite sequence of points over an interval", Proc. Kon. Ned. Akad. v. Wetensch.48, 266-271 (1945). Zbl0060.13002MR15143
  2. 2 Aardenne-Ehrenfest, T. van: "On the impossibility of a just distribution ", Proc. Kon. Ned. Akad. v. Wetensch.52, 734-739 (1949). Zbl0035.32002MR32717
  3. 3 Beck, J. and Chen, W.W.L.: Irregularities of Distribution (Cambridge University Press1987). Zbl0617.10039MR903025
  4. 4 Corput, J.G. van der: "Verteilungsfunktionen. I.", Proc. Kon. Ned. Akad. v. Wetensch.38, 813-821 (1935). Zbl0012.34705JFM61.0202.08
  5. 5 Halász, G.: "On Roth's method in the theory of irregularities of point distributions ", Recent Progress in Analytic Number Theory, vol. 2, pp. 79-94 (Academic Press, London, 1981). Zbl0459.10032MR637361
  6. 6 Hardy, G.H. and Littlewood, J.E.: "The lattice points of a right-angled triangle. I.", Proc. London Math. Soc.3(20), 15-36 (1922). Zbl48.0197.07JFM48.0197.07
  7. 7 Lerch, M.: "Question 1547", L'Intermédiaire Math.11, 145-146 (1904). 
  8. 8 Ostrowski, A.: "Bemerkungen zur Theorie der Diophantischen Approximationen. I.", Abh. Hamburg Sem.1, 77-98 (1922). Zbl48.0185.01JFM48.0185.01
  9. 9 Roth, K.F.: "On irregularities of distribution", Mathematika1, 73-79 (1954). Zbl0057.28604MR66435
  10. 10 Schmidt, W.M.: "Irregularities of distribution. VII.", Acta Arith.21, 45-50 (1972). Zbl0244.10035MR319933
  11. 11 Schmidt, W.M.: "Irregularities of distribution. X.", Number Theory and Algebra, pp. 311-329 (Academic Press, New York, 1977). Zbl0373.10020MR491574

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