Affine Sieve
  We establish the main saturation conjecture in [BGS10] connected with executing a Brun sieve in the setting of an orbit of a group of affine linear transformations. This is carried out under the condition that the Zariski closure of the group is Levi-semisimple. It is likely that this condition is also necessary for such saturation to hold. 
Alireza Salehi Golsefidy, Peter Sarnak
math.NT math.GR