Dirichlet's theorem and diophantine approximation on manifolds

We show that if M ⊂ R k belongs to a general class of smooth manifolds then, for almost all x ∈ M, Dirichlet's theorem on Diophantine approximation cannot be infinitely improved.

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Bibliographic Details
Published in	Journal of number theory Vol. 36; no. 1; pp. 85 - 88
Main Authors	Dodson, M.M, Rynne, B.P, Vickers, J.A.G
Format	Journal Article
Language	English
Published	Elsevier Inc 1990
Online Access	Get full text

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Summary:	We show that if M ⊂ R k belongs to a general class of smooth manifolds then, for almost all x ∈ M, Dirichlet's theorem on Diophantine approximation cannot be infinitely improved.
ISSN:	0022-314X 1096-1658
DOI:	10.1016/0022-314X(90)90006-D