Diophantine approximation with restricted numerators and denominators on semisimple groups

Alexander Gorodnik, Shirali Kadyrov

Published 2012-05-02, updated 2014-11-03Version 2

We consider the problem of Diophantine approximation on semisimple algebraic groups by rational points with restricted numerators and denominators and establish a quantitative approximation result for all real points in the group by rational points with any prescribed denominator and an almost prime numerator.