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 | |
| Publication status | Published - 4 Apr 2023 |
Bibliographical note
Funding Information:The authors were supported by a Mathematisches Forschungsinstitut Oberwolfach – Research in Pairs Grant. JMF was financially supported by an (EP/R015104/1) and a (RPG‐2019‐034). EPSRC Standard Grant Leverhulme Trust Research Project Grant
Publisher Copyright:
© 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
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