A Khintchine type theorem for affine subspaces
Number Theory
2020-02-18 v1
Abstract
We show that affine subspaces of Euclidean space are of Khintchine type for divergence under certain multiplicative Diophantine conditions on the parametrizing matrix. This provides evidence towards the conjecture that all affine subspaces of Euclidean space are of Khintchine type for divergence, or that Khintchine's theorem still holds when restricted to the subspace. This result is proved as a special case of a more general Hausdorff measure result from which the Hausdorff dimension of W(\tau) intersected with an appropriate subspace is also obtained.
Cite
@article{arxiv.2002.06221,
title = {A Khintchine type theorem for affine subspaces},
author = {Daniel C. Alvey},
journal= {arXiv preprint arXiv:2002.06221},
year = {2020}
}
Comments
17 pages, 2 figures