Diophantine approximation with restricted numerators and denominators on   semisimple groups
  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. 
Alexander Gorodnik and Shirali Kadyrov
math.DS math.NT