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

Date | Accepted/In press - 15 Jun 2021 |

Date | E-pub ahead of print - 12 Jul 2021 |

Date | Published (current) - 17 Sep 2021 |

Volume | 388 |

Number of pages | 33 |

Early online date | 12/07/21 |

Original language | English |

In this paper we develop an explicit method for studying the distribution of rational points near manifolds. As a consequence we obtain optimal lower bounds on the number of rational points of bounded height lying at a given distance from an arbitrary non-degenerate curve in $\mathbb{R}^n$. This generalises previous results for analytic non-degenerate curves. Furthermore, the main results are proved in the inhomogeneous setting. For $n \geq 3$, the inhomogeneous aspect is new even under the additional assumption of analyticity. Applications of the main distribution theorem also include the inhomogeneous Khintchine-Jarnik type theorem for divergence for arbitrary non-degenerate curves in $\mathbb{R}^n$.

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## Programme Grant-New Frameworks in metric Number Theory

Project: Research project (funded) › Research

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