How to split Dyson's transference inequality with the help of Wolfgang   Schmidt's parametric geometry of numbers
  In this paper we develop some of the ideas belonging to W.Schmidt and L.Summerer to define intermediate Diophantine exponents and split Dyson's transference inequality into a chain of inequalities for intermediate exponents. This splitting generalizes the analogous result of M.Laurent and Y.Bugeaud for Khintchine's transference inequalities. 
Oleg N. German
math.NT