HansGill, R. J. ; Raka, Madhu (1980) Some inequalities for nonhomogeneous quadratic forms Indian Journal of Pure and Applied Mathematics, 11 (1). pp. 6074. ISSN 00195588

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Abstract
For 0≤μ<1, functions f(μ) are obtained such that for any real indefinite quadratic form Q(x, y, z) of type (1,2) and determinant D and real x_{0}, y_{0}, z_{o}, the inequality μ(f(μ) D)⅓< Q(x + x_{0}, y + y_{0}, z + z_{0})<(f((μ) D)⅓ has a solution in integers x, y, z. This result is used to prove that for any real quaternary from Q(x,y. z, t) of type (1,3) and determinant D and real numbers x_{0}, y_{0}, z_{0}, t_{0}, the inequality 0<Q(x + x_{0}, y + y_{0}, z + z_{0}, t + t_{0})< 128/25(2√7I) IDI)^{¼} has a solution in integers x, y. z, and t.
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Deposited On:  19 Dec 2011 04:59 
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