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

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

Keywords

  • Quadratic Form
  • Quaternary Form
  • Primitive Lattice
  • Ternary Quadratic Form
  • Similar Lemma

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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.

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  Google Scholar 

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

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1982 Springer-Verlag

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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

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

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