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A problem of Good on Hausdorff dimension

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  26 February 2010

C. Ganesa Moorthy
C. Ganesa Moorthy
Affiliation:
Department of Mathematics, Alagappa University, Karaikudi-623 003, India.
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Extract

Given ξ in [0, 1] let ξ = [0, a1, a2…] denote a simple continued fraction expansion of ξ Given the expansion ξ = [0, a1, a2, …] let

Thus with the conventions p1 = q0 = 1 and q−1 = p0 = 0 we have

MSC classification

Secondary: 11J70: Continued fractions and generalizations
Type
Research Article
Information
Mathematika , Volume 39 , Issue 2 , December 1992 , pp. 244 - 246
Copyright
Copyright © University College London 1992

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References

1.Cusick, T. W.. Hausdorff dimension of sets of continued fractions. Quart. J. Math. Oxford (2), 41 (1990), 277–286.CrossRefGoogle Scholar
2.Good, I. J.. The fractional dimension theory of continued fractions. Proc. Camb. Phil Soc., 37 (1941), 199–228.CrossRefGoogle Scholar
3.Hirst, K. E.. A problem in the fractional dimension theory of continued fractions. Quart. J. Math. Oxford (2), 21 (1970), 29–35.CrossRefGoogle Scholar