In Homogeneous Approximation in the Field of formal Power Series

Abstract

A theorem of Khintchine (see e.g. Cassels [2]) states the following: For all pairs of integers m > 0, n > 0 there is a constant Γ_m, _n > 0 with the following property. Let L_j(X) (1 < j < n) be any real homogeneous linear forms in m variables (x₁ , . . , xm) = X.