Khinchin theorem for integral points on quadratic varieties

Details Khinchin theorem for integral points on quadratic varieties Khinchin theorem for integral points on quadratic varieties

2008-04-22

arxiv.org/abs/0804.3530v1

Mathematics

Number Theory

19 pages

Scientific paper

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.

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