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Singular n-tuples and Hausdorff dimension. II

Published online by Cambridge University Press:  24 October 2008

R. C. Baker
R. C. Baker
Affiliation:
Department of Mathematics, Royal Holloway and Bedford New College, Egham, Surrey TW20 OEX
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Extract

Let n be a natural number, with n ≥ 2. Let Kn denote the set of θ in Euclidean space Rn for which θ1, …, θn, 1 are linearly independent over the rational numbers. We denote points of the set of integer n-tuples Zn by x, y,…. We write

Inner product is denoted by θø. In Rl, ‖θ‖ denotes distance to the nearest integer.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 3 , May 1992 , pp. 577 - 584
Copyright
Copyright © Cambridge Philosophical Society 1992

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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]Davenport, H. and Schmidt, W. M.. Dirichlet's theorem on Diophantine approximation: II. Ada Arith. 16 (1970), 413–424.CrossRefGoogle Scholar
[3]Khintchine, A. Y.. Über eine Klasse linearer diophantischer Approximationen. Rend. Circ. Mat. Palermo 50 (1926), 170–195.CrossRefGoogle Scholar
[4]Rogers, C. A.. Hausdorff Measures (Cambridge University Press, 1970).Google Scholar
[5]Rynne, B. P.. A lower bound for the Hausdorff dimension of sets of singular n-tuples. Math. Proc. Cambridge Philos. Soc. 107 (1990), 387–394.CrossRefGoogle Scholar
[6]Rynne, B. P.. The Hausdorff dimension of certain sets of singular n-tuples. Math. Proc. Cambridge Philos. Soc. 108 (1990), 105–110.CrossRefGoogle Scholar
[7]Yavid, K. Y.. An estimate for the Hausdorff dimension of sets of singular vectors. Dokl. Akad. Nauk BSSR 31 (1987), 777–780.Google Scholar