二次曲面上的有理逼近:一个单纯形引理及其结果

L’Enseignement Mathématique Pub Date : 2018-08-21 DOI:10.4171/LEM/64-3/4-11

D. Kleinbock, Nicolas de Saxc'e

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引用次数: 5

摘要

在有理二次超曲面$X\子集\mathbb{P}^n(\mathbb{R})$上给出了最近几个关于内征丢芬图近似的结果的更强的初等证明。主要的工具是对单纯形引理的改进，它本质上说X$上彼此足够接近的有理点必须位于X$的一个完全各向同性的有理子空间上。

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Rational approximation on quadrics: A simplex lemma and its consequences

We give elementary proof of stronger versions of several recent results on intrinsic Diophantine approximation on rational quadric hypersurfaces $X\subset \mathbb{P}^n(\mathbb{R})$. The main tool is a refinement of the simplex lemma, which essentially says that rational points on $X$ which are sufficiently close to each other must lie on a totally isotropic rational subspace of $X$.

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L’Enseignement Mathématique

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