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ON THE DISTRIBUTION OF DENOMINATORS IN SYLVESTER EXPANSIONS

Published online by Cambridge University Press:  18 January 2002

JUN WU
Affiliation:
Department of Mathematics and Center of Non-linear Science, Wuhan University, 430072, Wuhan, People's Republic of China; wujunyu@public.wh.hb.cn
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Abstract

For any x ∈ (0, 1], let the series [sum ]n=1 1/dn(x) be the Sylvester expansion of x. Galambos has shown that the Lebesgue measure of the set

[formula here]

is 1 when α = e, the base of the natural logarithm. This paper provides a proof that for any α [ges ] 1, A(α) has Hausdorff dimension 1 when α ≠ e.

Type
NOTES AND PAPERS
Copyright
© The London Mathematical Society 2002

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