Intrinsic Diophantine approximation on circles and spheres

Byungchul Cha, Dong Han Kim

Research output: Contribution to journalArticlepeer-review

Abstract

We study Lagrange spectra arising from intrinsic Diophantine approximation of circles and spheres. More precisely, we consider three circles embedded in (Figure presented.) or (Figure presented.) and three spheres embedded in (Figure presented.) or (Figure presented.). We present a unified framework to connect the Lagrange spectra of these six spaces with the spectra of (Figure presented.) and (Figure presented.). Thanks to prior work of Asmus L. Schmidt on the spectra of (Figure presented.) and (Figure presented.), we obtain as a corollary, for each of the six spectra, the smallest accumulation point and the initial discrete part leading up to it completely.

Original languageEnglish
Article numbere12228
JournalMathematika
Volume70
Issue number1
DOIs
StatePublished - Jan 2024

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