Beresnevich, Victor orcid.org/0000-0002-1811-9697, Vaughan, R. C., Velani, Sanju orcid.org/0000-0002-4442-6316 et al. (1 more author) (2017) Diophantine Approximation on Manifolds and the Distribution of Rational Points: Contributions to the Convergence Theory. International Mathematics Research Notices. pp. 2885-2908. ISSN 1687-0247
Abstract
In this article, we develop the convergence theory of simultaneous, inhomogeneous Diophantine approximation on manifolds. A consequence of our main result is that if the manifold M ⊂ ℝ n is of dimension strictly greater than (n+1)/2 and satisfies a natural non-degeneracy condition, then M is of Khintchine type for convergence. The key lies in obtaining essentially the best possible upper bound regarding the distribution of rational points near manifolds.
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Copyright, Publisher and Additional Information: | © 2016, The Author(s). | ||||||
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Institution: | The University of York | ||||||
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) | ||||||
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Depositing User: | Pure (York) | ||||||
Date Deposited: | 15 Jun 2016 09:47 | ||||||
Last Modified: | 11 Feb 2024 00:20 | ||||||
Published Version: | https://doi.org/10.1093/imrn/rnv389 | ||||||
Status: | Published | ||||||
Refereed: | Yes | ||||||
Identification Number: | https://doi.org/10.1093/imrn/rnv389 | ||||||
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