The Metrical Theory of Simultaneously Small Linear Forms
Number Theory
2009-10-20 v1
Abstract
In this paper we investigate the metrical theory of Diophantine approximation associated with linear forms that are simultaneously small for infinitely many integer vectors; i.e. forms which are close to the origin. A complete Khintchine--Groshev type theorem is established, as well as its Hausdorff measure generalization. The latter implies the complete Hausdorff dimension theory.
Cite
@article{arxiv.0910.3428,
title = {The Metrical Theory of Simultaneously Small Linear Forms},
author = {Mumtaz Hussain and Jason Levesley},
journal= {arXiv preprint arXiv:0910.3428},
year = {2009}
}
Comments
15 pages