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**Int Math Res Notices-2016-Beresnevich-imrn_rnv389**198 KB, PDF document

Journal | International Mathematics Research Notices |
---|---|

Date | Accepted/In press - 23 Dec 2015 |

Date | E-pub ahead of print - 14 Jun 2016 |

Date | Published (current) - 1 May 2017 |

Issue number | 10 |

Volume | 2017 |

Number of pages | 24 |

Pages (from-to) | 2885-2908 |

Early online date | 14/06/16 |

Original language | English |

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.

© 2016, The Author(s).

## Programme Grant-New Frameworks in metric Number Theory

Project: Research project (funded) › Research

## Diophantine properties of Mahler´s numbers

Project: Research project (funded) › Research

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