Rational approximation of affine coordinate subspaces of Euclidean space
Volume 177 / 2017
Acta Arithmetica 177 (2017), 91-100
MSC: Primary 11J83, 11J13.
DOI: 10.4064/aa8521-8-2016
Published online: 2 December 2016
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.
