Inhomogeneous minimum of indefinite quadratic forms in five variables of type (3,2) or (2,3): a conjecture of watson

Hans-Gill, R. J. ; Raka, Madhu (1979) Inhomogeneous minimum of indefinite quadratic forms in five variables of type (3,2) or (2,3): a conjecture of watson Monatshefte fur Mathematik, 88 (4). pp. 305-320. ISSN 0026-9255

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Official URL: http://www.springerlink.com/content/nh7226w3555764...

Related URL: http://dx.doi.org/10.1007/BF01534249

Abstract

Let Q(x,y,z,t,u) be a real indefinite quadratic form in five variables of type (3,2) or (2,3) and determinant D ≠ 0. The given any real numbersx 0,y 0,z 0,t 0,u 0 we can find integers x,y,z,t,u, satisfying |Q(x + x0,y + y0,z + z0,t + t0,u + u0)| ≤ (¼|D|)1/5. All the cases when the sign of equality holds are also determined.

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