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arXiv · 2105.06776

Diophantine approximation in metric space

Jonathan M. Fraser·Henna Koivusalo·Felipe A. Ramirez
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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 Jarnik-Besicovitch type dimension bounds and investigate their sharpness.

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Jonathan M. Fraser, Henna Koivusalo, Felipe A. Ramirez. 2021-05-14. Diophantine approximation in metric space. https://arxiv.org/abs/2105.06776

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