Skip to main content

Some recent results on positive values of non-homogeneous indefinite quadratic forms

  • Conference paper
  • First Online:
Number Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 938))

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 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.99
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.

References

  1. R.P. Bambah, V.C. Dumir and R.J. Hans-Gill, (1981), On a conjecture of Jackson on non-homogeneous quadratic forms: J. Number Th. (to appear).

    Google Scholar 

  2. E.S. Barnes, (1961), The Positive values of inhomogeneous ternary quadratic forms. J. Austral. Math. Soc., 2, 127–132.

    Article  MathSciNet  MATH  Google Scholar 

  3. H. Blaney (1948), Indefinite quadratic forms in n variables, J. London Math. Soc., 23, 155–160.

    MathSciNet  MATH  Google Scholar 

  4. H. Blaney, (1950), Indefinite ternary quadratic forms, Quart. J. Math. Oxford Ser (2), 1, 262–269.

    Article  MathSciNet  MATH  Google Scholar 

  5. H. Devenport (1948), Non-homogeneous ternary quadratic forms, Acta. Math. 80, 65–95.

    Article  MathSciNet  Google Scholar 

  6. H. Devenport and H. Heilbronn (1947), A symmetric inequalities for non-homogeneous linear forms, J. London Math. Soc., 22, 53–61.

    Article  MathSciNet  Google Scholar 

  7. V.C. Dumir, (1968), Positive values of inhomogeneous quaternary quadratic forms, I and II, J. Aust. Math. Soc., 8, 87–101, 287–303.

    Article  MathSciNet  MATH  Google Scholar 

  8. V.C. Dumir and R.J. Hans-Gill, (1981), On positive values of non-homogeneous quarternary quadratic forms of type (1,3), Indian J. Pure and Appl. 12, 814–825.

    MathSciNet  MATH  Google Scholar 

  9. R.J. Hans-Gill and Madhu Raka (1980), Positive values of inhomogeneous 5-ary quadratic forms of type (3,2), J. Aust. Math. J. Soc. (A)

    Google Scholar 

  10. R.J. Hans-Gill and Madhu Raka, (1981), Positive values of inhomogeneous quadratic forms of type (4,1), J. Aust. Math. J. Soc. (A) 31 (to appear)

    Google Scholar 

  11. T.H. Jackson, (1969), Small Positive values of Indefinite quadratic forms, J. London Math. Soc. (2), 1, 643–659.

    Article  MathSciNet  MATH  Google Scholar 

  12. T.H. Jackson, (1971), Gaps between the values of quadratic forms, Proc. London. Math. Soc. 23, 267–282.

    Article  MathSciNet  Google Scholar 

  13. T.H. Jackson (1971), One sided inequalities for quaternary forms, Proc. London. Math. Soc. 23, 267–282.

    Article  MathSciNet  MATH  Google Scholar 

  14. A.M. Macbeath, (1951), A new sequence of minima in the geometry of number, Proc. Camb. Phil. Soc., 47, 266–273.

    Article  MathSciNet  MATH  Google Scholar 

  15. A. Oppenheim, (1931), The minima of indefinite quaternary quadratic forms, Annals Math. 32 271–298.

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Oppenheim, (1953a) Values of quadratic forms, I, II, Quart. J. Math. Oxford (2), 4, 54–59, 60–66.

    Article  MathSciNet  MATH  Google Scholar 

  17. A. Oppenheim, (1953b), Values of quadratic forms III, Monat. Math., 57, 97–101.

    Article  MathSciNet  MATH  Google Scholar 

  18. A. Oppenheim, (1953c), One sided inequalities for quadratic forms II, quaternary forms, PLMS(3), 3, 417–429.

    Article  MathSciNet  MATH  Google Scholar 

  19. G.L. Watson, (1960), Indefinite quadratic polynomials, Math. 7, 141–144.

    MathSciNet  MATH  Google Scholar 

  20. G.L. Watson, (1968), Asymmetric inequalities for indefinite quadratic forms, Proc. London. Math. Soc. (3) 18, 95–113.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Krishnaswami Alladi

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Hans-Gill, R.J. (1982). Some recent results on positive values of non-homogeneous indefinite quadratic forms. In: Alladi, K. (eds) Number Theory. Lecture Notes in Mathematics, vol 938. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097174

Download citation

  • DOI: https://doi.org/10.1007/BFb0097174

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11568-7

  • Online ISBN: 978-3-540-39279-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics