Spherical averages of Siegel transforms for higher rank diagonal actions   and applications
  We investigate the geometry of approximates in multiplicative Diophantine approximation. Our main tool is a new multiparameter averaging result for Siegel transforms on the space of unimodular lattices in ${\mathbb R}^n$ which is of independent interest. 
Jayadev S. Athreya, Anish Ghosh, Jimmy Tseng
math.DS math.NT