Bounded representations of the positive values of an indefinite quadratic form
1958 ◽
Vol 54
(1)
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pp. 14-17
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Keyword(s):
Letbe a real quadratic form in n variables (n ≥ 2) with integral coefficients and determinant D = |fij| ≠ 0. Cassels ((1),(2)) has recently proved that if the equation f = 0 is properly soluble in integers x1, …, xn, then there is a solution satisfyingwhere F = max | fij and cn depends only on n. An example given by Kneser (see (2)) shows that the exponent ½(n – 1) is best possible. A simpler proof of Cassels's result has since been given by Davenport(3), and the theorem has been improved in certain cases by Watson(4). Here I consider the inequality f(x1, …, xn) > 0, where f is an indefinite form, and obtain a result analogous to that of Cassels.
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):
1963 ◽
Vol 15
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pp. 412-421
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1983 ◽
Vol 94
(1)
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pp. 1-8
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1968 ◽
Vol 8
(2)
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pp. 287-303
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1968 ◽
Vol 8
(1)
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pp. 87-101
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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):
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
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