Linear subspaces and the angles of inclination: contribution to W.M. Schmidt's theory

12.02.2019 13:15 - 14:45

Nikolay Moshchevitin, Moscow Lomonosov State University

We prove a metric statement about approximation of  a \(n\)-dimensional linear subspace \(A\) in \(\mathbb{R}^d\) by \(n\)-dimensional rational subspaces. We consider the problem of finding rational subspace \(B\)  of bounded height \(H=H(B)\) for which the angle of inclination \(\psi (A,B) \) is small in terms of \(H\). In the simplest case \(d=4, n=2\) we give a partial solution of a problem formulated by W.M. Schmidt in 1967.


H. Grobner, A. Minguez-Espallargas, A. Mellit


SR 01, EG, OMP 1