Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-16T16:08:27.407Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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