An upper estimate for the product linear nonhomogeneous forms for lattices with a small homogeneous minimum

One obtains the following transfer theorem, related to Minkowski's nonhomogeneous conjecture. Let Λ ? ?ⁿ be a point lattice, det Λ=1. We consider the nonhomogeneous Π(Λ) and the homogeneous L(Λ)=бⁿ. б ? 0, arithmetical minima of the lattice Λ. Then for sufficiently largen, if , then .