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arXiv · 1808.07070

Rational approximation on quadrics: a simplex lemma and its consequences

Dmitry Kleinbock·Nicolas de Saxcé
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Abstract

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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Dmitry Kleinbock, Nicolas de Saxcé. 2018-08-21. Rational approximation on quadrics: a simplex lemma and its consequences. https://arxiv.org/abs/1808.07070

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