Skip to main content

Resultats nouveaux dans la theorie quantitative de l’equirepartition

  • Conference paper
  • First Online:
Répartition Modulo 1

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 475))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Références

  1. Bauer, W.: Diskrepanz in separablen metrischen Räumen, Monatsh. Math., à paraitre.

    Google Scholar 

  2. Billingsley, P.— Topsøe, F.: Uniformity in weak convergence, Z. Wahrscheinlichkeitsth. 7, 1–16 (1967).

    Article  MATH  MathSciNet  Google Scholar 

  3. Borwein, D.: On a scale of Abel-type summability methods, Proc. Cambridge Phil. Soc., 53, 318–322 (1957).

    Article  MATH  MathSciNet  Google Scholar 

  4. Elliott, P. D. T. A.: On distribution functions (mod 1): Quantitative Fourier inversion, J. Number Th. 4, 509–522 (1972).

    Article  MATH  MathSciNet  Google Scholar 

  5. Fréchet, M.: Généralités sur les probabilités. Eléments aléatoires, 2e éd., Gauthier-Villars, Paris, 1950.

    MATH  Google Scholar 

  6. Hiawka, E.: Discrepancy and Riemann integration, Studies in Pure Mathematics (L. Mirsky, ed.), pp. 121–129, Academic Press, New York, 1971.

    Google Scholar 

  7. -: Über eine Methode von E. Hecke in der Theorie der Gleichverteilung, Acta Arith. 24, 11–31 (1973).

    MathSciNet  Google Scholar 

  8. Kuipers, L.— Niederreiter, H.: Uniform Distribution of Sequences, Interscience Tracts, John Wiley and Sons, New York, 1974.

    MATH  Google Scholar 

  9. Lesca, J.: Sur la répartition modulo 1 de la suite nα, Acta Arith. 20, 345–352 (1972).

    MATH  MathSciNet  Google Scholar 

  10. Meijer, H. G.: On a distribution problem in finite sets, Indag. Math. 35, 9–17 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  11. Meijer, H. G.— Niederreiter, H.: On a distribution problem in finite sets, Compositio Math. 25, 153–160 (1972).

    MATH  MathSciNet  Google Scholar 

  12. Meijer, H. G.— Niederreiter, H.: Equirépartition et théorie des nombres premiers, dans ce volume.

    Google Scholar 

  13. Mück, R.— Philipp, W.: Distances of probability measures and uniform distribution mod 1, Math. Z., à paraitre.

    Google Scholar 

  14. Niederreiter, H.: Almost-arithmetic progressions and uniform distribution, Trans. Amer. Math. Soc. 161, 283–292 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  15. -: Discrepancy and convex programming, Ann. Mat. Pura Appl. (IV) 93, 89–97 (1972).

    Article  MATH  MathSciNet  Google Scholar 

  16. -: On a number-theoretical integration method, Aequationes Math. 8, 304–311 (1972).

    Article  MATH  MathSciNet  Google Scholar 

  17. -: On the existence of uniformly distributed sequences in compact spaces, Compositio Math. 25, 93–99 (1972).

    MATH  MathSciNet  Google Scholar 

  18. -: Methods for estimating discrepancy, Applications of Number Theory to Numerical Analysis (S. K. Zaremba, ed.), pp. 203–236, Academic Press, New York, 1972.

    Chapter  Google Scholar 

  19. -: A distribution problem in finite sets, Applications of Number Theory to Numerical Analysis (S. K. Zaremba, ed.), pp. 237–248, Academic Press, New York, 1972.

    Chapter  Google Scholar 

  20. -: On the distribution of pseudo-random numbers generated by the linear congruential method, Math. Comp. 26, 793–795 (1972).

    Article  MATH  MathSciNet  Google Scholar 

  21. -: The distribution of Farey points, Math. Ann. 201, 341–345 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  22. -: Zur quantitativen Theorie der Gleichverteilung, Monatsh. Math. 77, 55–62 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  23. -: Metric theorems on the distribution of sequences, Proc. Symp. Pure Math., vol. XXIV, pp. 195–212, Amer. Math. Soc., Providence, R. I., 1973.

    MATH  Google Scholar 

  24. -: Application of diophantine approximations to numerical integration, Diophantine Approximation and Its Applications, (C. F. Osgood, ed.), pp. 129–199, Academic Press, New York, 1973.

    Google Scholar 

  25. Niederreiter, H.: On the distribution of pseudo-random numbers generated by the linear congruential method. II, Math. Comp., à paraître.

    Google Scholar 

  26. Niederreiter, H.: Quantitative versions of a result of Hecke in the theory of uniform distribution mod 1, Acta Arith., à paraître.

    Google Scholar 

  27. Niederreiter, H.: Well distributed sequences with respect to systems of convex sets, à paraitre.

    Google Scholar 

  28. Niederreiter, H.: Some new exponential sums with applications to pseudo-random numbers, Colloquium on Number Theory (Debrecen, 1974), North-Holland Publ. Co., Amsterdam, à paraitre.

    Google Scholar 

  29. Niederreiter, H.: On the distribution of pseudo-random numbers generated by the linear congruential method. III, à paraître.

    Google Scholar 

  30. Niederreiter, H.— Philipp, W.: Berry-Esseen bounds and a theorem of Erdös and Turán on uniform distribution mod 1, Duke Math. J. 40, 633–649 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  31. Philipp, W.: Limit theorems for lacunary series and uniform distribution mod 1, Acta Arith., à paraître.

    Google Scholar 

  32. Schmidt, W. M.: Irregularities of distribution. VII, Acta Arith. 21, 45–50 (1972).

    MATH  MathSciNet  Google Scholar 

  33. Schmidt, W. M.: Irregularities of distribution. VIII, Trans. Amer. Math. Soc., à paraître.

    Google Scholar 

  34. Tijdeman, R.: On a distribution problem in finite and countable sets, J. Combinatorial Theory Ser. A 15, 129–137 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  35. Warnock, T. T.: Computational investigations of low-discrepancy point sets, Applications of Number Theory to Numerical Analysis (S. K. Zaremba, ed.), pp. 319–343, Academic Press, New York, 1972.

    Chapter  Google Scholar 

  36. Zaremba, S. K.: La discrépance isotrope et l’intégration numérique, Ann. Mat. Pura Appl. (IV) 87, 125–136 (1970).

    Article  MATH  MathSciNet  Google Scholar 

  37. -: La méthode des “bon treillis” pour le calcul numérique des intégrales multiples, Applications of Number Theory to Numerical Analysis (S. K. Zaremba, ed.), pp. 39–119, Academic Press, New York, 1972.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Gérard Rauzy

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer-Verlag

About this paper

Cite this paper

Niederreiter, H. (1975). Resultats nouveaux dans la theorie quantitative de l’equirepartition. In: Rauzy, G. (eds) Répartition Modulo 1. Lecture Notes in Mathematics, vol 475. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074263

Download citation

  • DOI: https://doi.org/10.1007/BFb0074263

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07388-8

  • Online ISBN: 978-3-540-37579-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics