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arXiv · 0910.3428

The Metrical Theory of Simultaneously Small Linear Forms

Mumtaz Hussain·Jason Levesley
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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.

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Mumtaz Hussain, Jason Levesley. 2009-10-19. The Metrical Theory of Simultaneously Small Linear Forms. https://arxiv.org/abs/0910.3428

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