Proof of W.M.Schmidt's conjecture concerning successive minima of a lattice

Nikolay G. Moshchevitin

For a real $N\ge 1$ and a vector $\xi =(1,{\xi }_1,...,{\xi }_n)$ define a matrix $$ {\cal A} (ξ, N) = ({array}{ccccc} N^{-1} & 0& 0& ... &0 \cr N^{\frac{1}{n}} ξ_1 & -N^{\frac{1}{n}} & 0&... &…