On transfer inequalities in Diophantine approximation, II
On transfer inequalities in Diophantine approximation, II
复制标题
关于丢番图近似中的传递不等式，II
DOI：
--
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
M. Laurent
中科院分区：
文献类型：
--
作者：
Y. Bugeaud;M. Laurent
设Θ是Rn中的点。我们关注的是维数为d的有理线性子簇对Θ的逼近，其中0 ≤ d ≤ n−1。为此，我们在Grassmann代数Λ（Rn+1）中引入了各种凸体。结果是，我们的d次凸体是，在马勒意义下，1次凸体的第d个复合体。还给出了一个对偶公式。这种方法使我们能够分裂和完善经典的欣钦移情原理。
Let Θ be a point in Rn. We are concerned with the approximation to Θ by rational linear subvarieties of dimension d for 0 ≤ d ≤ n−1. To that purpose, we introduce various convex bodies in the Grassmann algebra Λ(Rn+1). It turns out that our convex bodies in degree d are the dth compound, in the sense of Mahler, of convex bodies in degree one. A dual formulation is also given. This approach enables us both to split and to refine the classical Khintchine transference principle.