Skip to main content

Waring's problem for sets of density zero

Part of the Lecture Notes in Mathematics book series (LNM,volume 899)

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.95
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. T. Bateman, On the representations of a number as the sum of three squares, Trans. Amer. Math. Soc. 71 (1951), 70–101.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. S. L. G. Choi, P. Erdös, and M. B. Nathanson, Lagrange's theorem with N1/3 squares, Proc. Amer. Math. Soc. 79 (1980), 203–205.

    MathSciNet  MATH  Google Scholar 

  3. P. Erdös and M. B. Nathanson, Lagrange's theorem and thin subsequences of squares, in J. Gani and V. K. Rohatgi, editors, Contributions to Probability: A Collection of Papers Dedicated to Eugene Lukacs, Academic Press, New York, 1981.

    Google Scholar 

  4. P. Erdös and A. Rényi, Additive properties of random sequences of positive integers, Acta. Arithm. 6 (1960), 83–110.

    MathSciNet  MATH  Google Scholar 

  5. H. Halberstam and K. F. Roth, Sequences Vol. I, Clarendon Press, Oxford, 1966.

    MATH  Google Scholar 

  6. G. H. Hardy and J. E. Littlewood, Some problems of ‘Partitio Numerorum': IV. The singular series in Waring's Problem and the value of the number G(k), Math. Zeit, 12 (1922), 161–188.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. D. Hilbert, Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n-ter Potenzen (Waringsche Problem), Math. Ann. 67 (1909), 281–300.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. L. G. Shnirel'man, On additive properties of integers, Izvestiyakh Donskogo Instituta v Novocherkasske 14 (1930), 3–27.

    Google Scholar 

  9. C. L. Siegel, Über die Klassenzahl quadratische Zahlkörper, Acta Arith. 1 (1935), 83–86.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Additional information

Dedicated to Emil Grosswald

Rights and permissions

Reprints and Permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Nathanson, M.B. (1981). Waring's problem for sets of density zero. In: Knopp, M.I. (eds) Analytic Number Theory. Lecture Notes in Mathematics, vol 899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096469

Download citation

  • DOI: https://doi.org/10.1007/BFb0096469

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11173-3

  • Online ISBN: 978-3-540-38953-8

  • eBook Packages: Springer Book Archive