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The asymmetric product of three inhomogeneous linear forms

Published online by Cambridge University Press:  09 April 2009

V. K. Grover
V. K. Grover
Affiliation:
Centre for Advanced Study in Mathematics, Panjab UniversityChandigarh-160 014, India
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Abstract

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Let Λ be a lattice in R3 of determinant 1. Define the homogeneous minium of Λ as mn (Λ) = inf |u1, u2, u3| extended over all points (u1, u2, u3) of Λ other than the origin. It is shown that for any given (c1, c2, c3) in R3 there exists a point (u1, u2, u3) of Λ for which provided that ρσ > 1/64 if mn (Λ) = 0, and ρσ ≥1/16.81 if mn (A) > 0.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 2 , April 1989 , pp. 236 - 250
Copyright
Copyright © Australian Mathematical Society 1989

References

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