A short proof of Minkowski's second theorem and its application to some   open questions
  In this paper we present a surprisingly short proof of Minkowski's second theorem. The author hopes there is no mistake in it, though the argument seems to be too plain to contain one. Also, we apply the main construction of the proof to some problems concerning the anomaly of a convex body, the density of the densest lattice packing, lattice point enumerator, and Ehrhart polynomial. 
Oleg N. German
math.NT