The Metrical Theory of Simultaneously Small Linear Forms

Details The Metrical Theory of Simultaneously Small Linear Forms The Metrical Theory of Simultaneously Small Linear Forms

2009-10-19

arxiv.org/abs/0910.3428v1

Mathematics

Number Theory

15 pages

Scientific paper

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.

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