Khinchin theorem for integral points on quadratic varieties
arXiv:0804.3530 · doi:10.1007/s00208-010-0561-z
Abstract
We prove an analogue the Khinchin theorem for the Diophantine approximation by integer vectors lying on a quadratic variety. The proof is based on the study of a dynamical system on a homogeneous space of the orthogonal group. We show that in this system, generic trajectories visit a family of shrinking subsets infinitely often.
19 pages