Quantitative rational approximation on spheres
Number Theory
2022-08-01 v4 Dynamical Systems
Abstract
We prove a quantitative theorem for Diophantine approximation by rational points on spheres. Our results are valid for arbitrary unimodular lattices and we further prove 'spiraling' results for the direction of approximates. These results are quantitative generalizations of the Khintchine-type theorem on spheres proved by Kleinbock and Merrill.
Keywords
Cite
@article{arxiv.2003.02243,
title = {Quantitative rational approximation on spheres},
author = {Mahbub Alam and Anish Ghosh},
journal= {arXiv preprint arXiv:2003.02243},
year = {2022}
}
Comments
Siegel's mean value theorem for the SO(n+1, 1) action on the light-cone elaborated