Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions

2002/10/18 by V. Bernik, D. Kleinbock, G. A. Margulis · 1 citation
Mathematics · #math.NT #math.DS #msc:11J83

paper · pdf

published as Internat. Math. Res. Notices. 2001, no. 9, 453--486 · 27 pages

arxiv created 2002/10/18 · arxiv updated 2009/11/30

Abstract

An analogue of the convergence part of the Khintchine-Groshev theorem, as well as its multiplicative version, is proved for nondegenerate smooth submanifolds in ℝⁿ. The proof combines methods from metric number theory with a new approach involving the geometry of lattices in Euclidean spaces.

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• Twisted Diophantine approximation on manifolds

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