Rational approximation of affine coordinate subspaces of Euclidean space
Number Theory
2017-08-09 v2
Abstract
We show that affine coordinate subspaces of dimension at least two in Euclidean space are of Khintchine type for divergence. For affine coordinate subspaces of dimension one, we prove a result which depends on the dual Diophantine type of the basepoint of the subspace. These results provide evidence for the conjecture that all affine subspaces of Euclidean space are of Khintchine type for divergence.
Keywords
Cite
@article{arxiv.1510.05012,
title = {Rational approximation of affine coordinate subspaces of Euclidean space},
author = {Felipe A. Ramírez and David S. Simmons and Fabian Süess},
journal= {arXiv preprint arXiv:1510.05012},
year = {2017}
}
Comments
10 pages. v2: new introduction