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Positive values of non-homogeneous indefinite quadratic forms of type (1, 4)

  • Madhu Raka
  • Urmila Rani
Article

Abstract

Let Гr,n—r denote the infimum of all number Г > 0 such that for any real indefinite quadratic form inn variables of type (r, n—r), determinantD ≠ 0 and real numbers c1; c2,…, cn, there exist integersx 1,x2,…,xn satisfying 0 < Q(x1+c1,x2 + c2,…,xn + cn) ≤(Г¦Z > ¦)1/n. All the values of Гr,n—r are known except for г1,4. Earlier it was shown that 8 ≤Г1,4 ≤16. Here we improve the upper bound to get Г1,4 < 12.

Keywords

Equivalent forms reduction soluble 

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References

  1. [1]
    Dumir V C and Sehmi Ranjeet, Positive values of non-homogeneous indefinite quadratic forms of type (1,4),Proc. Indian Acad, Sci. 104 (1994) 557–579MATHCrossRefGoogle Scholar
  2. [2]
    Jackson T H, Gaps between values of quadratic forms,J. London Math. Soc. 3 (1971) 47–58MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Indian Academy of Sciences 1997

Authors and Affiliations

  • Madhu Raka
    • 1
  • Urmila Rani
    • 1
  1. 1.Department of MathematicsPanjab UniversityChandigarhIndia

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