Intrinsic Diophantine approximation on circles and spheres

Abstract

AbstractWe study Lagrange spectra arising from intrinsic Diophantine approximation of circles and spheres. More precisely, we consider three circles embedded in or and three spheres embedded in or . We present a unified framework to connect the Lagrange spectra of these six spaces with the spectra of and . Thanks to prior work of Asmus L. Schmidt on the spectra of and , 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.