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 vect...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 $\mathcal{M}$ .展开更多
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)
文摘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 $\mathcal{M}$ .
