Rational approximation on quadrics: A simplex lemma and its consequences
Dmitry Kleinbock
Brandeis University, Waltham, USANicolas de Saxcé
Université Paris 13, Sorbonne Paris Cité, Villetaneuse, France
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Abstract
We give elementary proofs of stronger versions of several recent results on intrinsic Diophantine approximation on rational quadric hypersurfaces . The main tool is a refinement of the simplex lemma, which essentially says that rational points on which are sufficiently close to each other must lie on a totally isotropic rational subspace of .
Cite this article
Dmitry Kleinbock, Nicolas de Saxcé, Rational approximation on quadrics: A simplex lemma and its consequences. Enseign. Math. 64 (2018), no. 3/4, pp. 459–476
DOI 10.4171/LEM/64-3/4-11