Projects per year
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 $\mathbb{R}^n$. 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 $\mathbb{R}^n$.
Original language | English |
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Article number | 107861 |
Number of pages | 33 |
Journal | Advances in Mathematics |
Volume | 388 |
Early online date | 12 Jul 2021 |
DOIs | |
Publication status | Published - 17 Sept 2021 |
Bibliographical note
© 2021 Published by Elsevier Inc. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.Projects
- 1 Finished
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Programme Grant-New Frameworks in metric Number Theory
1/06/12 → 30/11/18
Project: Research project (funded) › Research