Positive values of inhomogeneous quaternary ouadratic forms, II
1968 ◽
Vol 8
(2)
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pp. 287-303
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Keyword(s):
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
1981 ◽
Vol 89
(2)
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pp. 225-235
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1983 ◽
Vol 94
(1)
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pp. 9-22
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Keyword(s):
1983 ◽
Vol 94
(1)
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pp. 1-8
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1968 ◽
Vol 8
(1)
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pp. 87-101
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Keyword(s):
1967 ◽
Vol 63
(2)
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pp. 277-290
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1948 ◽
Vol 44
(4)
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pp. 457-462
Keyword(s):
1963 ◽
Vol 15
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pp. 412-421
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1958 ◽
Vol 54
(1)
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pp. 14-17
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Keyword(s):
1948 ◽
Vol 44
(2)
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pp. 145-154
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1961 ◽
Vol 2
(1)
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pp. 9-10
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Keyword(s):