## Abstract

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 R^{n}. This generalises previous results for analytic non-degenerate curves. Furthermore, the main results are proved in the inhomogeneous setting. For n≥3, the inhomogeneous aspect is new even under the additional assumption of analyticity. Applications of the main distribution theorem also include the inhomogeneous Khintchine-Jarník type theorem for divergence for arbitrary non-degenerate curves in R^{n}.

Original language | English (US) |
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Article number | 107861 |

Journal | Advances in Mathematics |

Volume | 388 |

DOIs | |

State | Published - Sep 17 2021 |

## All Science Journal Classification (ASJC) codes

- General Mathematics