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A lower bound for the Hausdorff dimension of sets of singular n-tuples

Published online by Cambridge University Press:  24 October 2008

Bryan P. Rynne
Bryan P. Rynne
Affiliation:
Department of Mathematics and Computer Science, University of Dundee, Dundee DD1 4HN, Scotland
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Extract

In this paper we improve the estimate for the lower bound of the Hausdorff dimension of certain sets of singular n-tuples in ℝn obtained by Baker in [1]. We begin with a brief discussion of the problem. More details can be found in [1]. For ease of comparison with Baker's results we will adopt a similar notation to that of [1].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 2 , March 1990 , pp. 387 - 394
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

REFERENCES

[1]Baker, R. C.. Singular n-tuples and Hausdorff dimension. Math. Proc. Cambridge Philos. Soc. 81 (1977), 377–385.CrossRefGoogle Scholar
[2]Cassels, J. W. S.. An Introduction to Diophantine Approximation (Cambridge University Press, 1965).Google Scholar
[3]Khintchine, A. Y.. Über eine Klasse linearer Diophantischer Approximationen. Rend. Circ. Mat. Palermo 50 (1926), 170–195.CrossRefGoogle Scholar
[4]Yavid, K. Y.. An estimate for the Hausdorff dimension of sets of singular vectors. Dokl. Akad. Nauk BSSR 31 (1987), 777–780.Google Scholar