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Positive values of inhomogeneous quaternary ouadratic forms, II

Published online by Cambridge University Press:  09 April 2009

Vishwa Chander Dumir
Vishwa Chander Dumir
Affiliation:
University of Illinois Urbana, Illinois
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In a previous paper [4] we showed that Γ3,1 = 16/. For the definition of Γr, s for an indefinite quadratic form in n = r + s variables of the type (r, s) see the above paper. Here we shall show that Γ2,2 = 16. More precisely we prove:Theorem. Let Q (x, y, z, t) be an indefinite quaternary quadratic form with determinant D > 0 and signature (2, 2). Then given any real numbers x0, y0, z0, t0 we can find integers x, y, z, t such thatEquality is necessary if and only if either where ρ ≠ 0. For Q1 equality occurs if and only if

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 2 , May 1968 , pp. 287 - 303
Copyright
Copyright © Australian Mathematical Society 1968

References

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