In this paper we consider the probabilistic theory of Diophantine approximation in projective space over a completion of . Using the projective metric studied in [Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 23 (1996), no. 2, 211–248] we prove the analogue of Khintchine's theorem in projective space. For finite places and in higher dimension, we are able to completely remove the condition of monotonicity and establish the analogue of the Duffin–Schaeffer conjecture.
|Number of pages||12|
|Journal||Journal für die reine und angewandte Mathematik (Crelles Journal)|
|Early online date||31 Oct 2013|
|Publication status||Published - Mar 2016|