Diophantine approximation in metric space

Jonathan Fraser, Henna Koivusalo, Felipe Ramirez*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)756-776
Number of pages21
JournalBulletin of the London Mathematical Society
Volume55
Issue number2
Early online date2 Dec 2022
DOIs
Publication statusPublished - 1 Apr 2023

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