On the transference principle and Nesterenko's linear independence criterion

We consider the problem of simultaneous approximation real numbers $\theta_1, …,\theta_n$ by rationals and dual approximating zero values linear form $x_0+\theta_1x_1+…+\theta_nx_n$ at integer points. In this setting we analyse two transference inequalities obtained Schmidt Summerer. present a rather simple geometric observation which proves their result. also derive several previously unknown corollaries. particular, show that, together with German's for uniform exponents, Summerer's imply Bugeaud Laurent "one half" Marnat Moshchevitin. Moreover, that our main construction provides proof Nesterenko's independence criterion.