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ON THE DISTRIBUTION OF DENOMINATORS IN SYLVESTER EXPANSIONS
Published online by Cambridge University Press: 18 January 2002
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.
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- © The London Mathematical Society 2002
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