By the same authors

From the same journal

Diophantine Approximation on Manifolds and the Distribution of Rational Points: Contributions to the Convergence Theory

Research output: Contribution to journalArticlepeer-review

Full text download(s)


Published copy (DOI)



Publication details

JournalInternational Mathematics Research Notices
DateAccepted/In press - 23 Dec 2015
DateE-pub ahead of print - 14 Jun 2016
DatePublished (current) - 1 May 2017
Issue number10
Number of pages24
Pages (from-to)2885-2908
Early online date14/06/16
Original languageEnglish


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.

Bibliographical note

© 2016, The Author(s).


Discover related content

Find related publications, people, projects, datasets and more using interactive charts.

View graph of relations