Diophantine approximation on rational quadrics
Group Theory
2007-05-23 v2 Number Theory
Abstract
We compute the Hausdorff dimension of sets of very well approximable vectors on rational quadrics. We use ubiquitous systems and the geometry of locally symmetric spaces. As a byproduct we obtain the Hausdorff dimension of the set of rays with a fixed maximal singular direction, which move away into one end of a locally symmetric space at linear depth, infinitely many times.
Cite
@article{arxiv.math/0503606,
title = {Diophantine approximation on rational quadrics},
author = {Cornelia Drutu},
journal= {arXiv preprint arXiv:math/0503606},
year = {2007}
}
Comments
55 pages, 3 figures, to appear in Math. Annalen, revised version : updated references, minor corrections