Diophantine approximation in metric space
Number Theory
2024-03-20 v1 Classical Analysis and ODEs
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 Jarnik-Besicovitch type dimension bounds and investigate their sharpness.
Cite
@article{arxiv.2105.06776,
title = {Diophantine approximation in metric space},
author = {Jonathan M. Fraser and Henna Koivusalo and Felipe A. Ramirez},
journal= {arXiv preprint arXiv:2105.06776},
year = {2024}
}
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17 pages