Simultaneous Diophantine Approximation in Non-degenerate p-adic   Manifolds
  S-arithmetic Khintchine-type theorem for products of non-degenerate analytic p-adic manifolds is proved for the convergence case. In the p-adic case the divergence part is also obtained. 
Amir Mohammadi, Alireza Salehi Golsefidy
math.NT math.DS