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Journal | Advances in Mathematics |
---|---|

Date | Accepted/In press - 4 Jul 2016 |

Date | E-pub ahead of print - 27 Jul 2016 |

Date | Published (current) - 22 Oct 2016 |

Volume | 302 |

Number of pages | 49 |

Pages (from-to) | 231-279 |

Early online date | 27/07/16 |

Original language | English |

This paper is motivated by recent applications of Diophantine approximation in electronics, in particular, in the rapidly developing area of Interference Alignment. Some remarkable advances in this area give substantial credit to the fundamental Khintchine-Groshev Theorem and, in particular, to its far reaching generalisation for submanifolds of a Euclidean space. With a view towards the aforementioned applications, here we introduce and prove quantitative explicit generalisations of the Khintchine-Groshev Theorem for non-degenerate submanifolds of R
^{n}. The importance of such quantitative statements is explicitly discussed in Jafar's monograph [12, §4.7.1].

©2016 The Author(s). Published by Elsevier Inc

- Khintchine-Groshev Theorem, Metric Diophantine approximation, Non-degenerate manifolds

## Programme Grant-New Frameworks in metric Number Theory

Project: Research project (funded) › Research

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