摘要
Let $\mathcal{M}$ be an m-dimensional analytic manifold in ? n . In this paper, we prove that almost all vectors in $\mathcal{M}$ (in the sense of Lebesgue measure) are Diophantine if there exists one Diophantine vector in $\mathcal{M}$ .
Let M be an m-dimensional analytic manifold in R^n.In this paper,we prove that almost all vectors in M (in the sense of Lebesgue measure) are Diophantine if there exists one Diophantine vector in M.
基金
This work was partially supported by the National Natural Science Foundation of China (Grant No.10531050)
the National Basic Research Program of China (Grant No.2007CB814800)
