Diophantine approximation on rational quadrics

Details Diophantine approximation on rational quadrics Diophantine approximation on rational quadrics

2005-03-25

arxiv.org/abs/math/0503606v2

Mathematics

Group Theory

55 pages, 3 figures, to appear in Math. Annalen, revised version : updated references, minor corrections

Scientific paper

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.

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