Diophantine Approximation in Metric Space

Öffnen
Datum
2021-06-14MFO Scientific Program
Research in Pairs 2020Serie
Oberwolfach Preprints;2021-07Autor
Fraser, Jonathan M.
Koivusalo, Henna
Ramírez, Felipe A.
Metadata
Zur LanganzeigeOWP-2021-07
Zusammenfassung
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