Diophantine approximation in metric space
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.
Citation
Fraser , J , Koivusalo , H & Ramirez , F 2023 , ' Diophantine approximation in metric space ' , Bulletin of the London Mathematical Society , vol. 55 , no. 2 , pp. 756-776 . https://doi.org/10.14760/OWP-2021-07 , https://doi.org/10.1112/blms.12755
Publication
Bulletin of the London Mathematical Society
Status
Peer reviewed
ISSN
0024-6093Type
Journal article
Description
Funding: The authors were supported by a Mathematisches Forschungsinstitut Oberwolfach - Research in Pairs Grant. JMF was financially supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034).Collections
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