The asymmetric product of three inhomogeneous linear forms

Abstract

AbstractLet 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.