Diophantine approximation in metric space

Jonathan Fraser; Henna Koivusalo; Felipe Ramirez

doi:10.14760/OWP-2021-07

Diophantine approximation in metric space

Jonathan Fraser, Henna Koivusalo, Felipe Ramirez^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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Abstract

Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are replaced with a countable hierarchy of “well-spread” points, which we refer to as abstract rationals. We prove various Jarník–Besicovitch type dimension bounds and investigate their sharpness.

Original language	English
Pages (from-to)	756-776
Number of pages	21
Journal	Bulletin of the London Mathematical Society
Volume	55
Issue number	2
Early online date	2 Dec 2022
DOIs	https://doi.org/10.14760/OWP-2021-07 https://doi.org/10.1112/blms.12755
Publication status	Published - 1 Apr 2023

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Copyright © 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1112/blms.12755.
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New perspectives in the dimension: New perspectives in the dimension theory of fractals
Fraser, J. (PI)
The Leverhulme Trust
1/09/19 → 31/01/23
Project: Standard
Fourier analytic techniques: Fourier analytic techniques in geometry and analysis
Fraser, J. (PI) & Falconer, K. J. (CoI)
EPSRC
1/02/18 → 11/06/21
Project: Standard

Cite this

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Diophantine approximation in metric space

Abstract

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New perspectives in the dimension: New perspectives in the dimension theory of fractals

Fourier analytic techniques: Fourier analytic techniques in geometry and analysis

Cite this