Diophantine vectors in analytic submanifolds of Euclidean spaces

作     者：Rong-mei CAO~(1+) Jian-gong YOU~2 1 College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China 2 Department of Mathematics,Nanjing University,Nanjing 210093,China 

作者机构：College of Science Nanjing University of Aeronautics and Astronautics Nanjing China Department of Mathematics Nanjing University Nanjing China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2007年第50卷第9期

页      面：1334-1338页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

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) 

主　　题：diophantine vector analytic submanifold 32C05 

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 $\mathcal{M}$ .