An iterated logarithm law related to decimal and continued fraction expansions |
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Authors: | Jun Wu |
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Institution: | (1) Huazhong University of Science and Technology, Hubei, P.R. China |
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Abstract: | For an irrational number x and n ≥ 1, we denote by k
n
(x) the exact number of partial quotients in the continued fraction expansion of x given by the first n decimals of x. G. Lochs proved that for almost all x, with respect to the Lebesgue measure
In this paper, we prove that an iterated logarithm law for {k
n
(x): n ≥ 1}, more precisely, for almost all x,
for some constant σ > 0.
Author’s address: Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P.R. China |
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Keywords: | 2000 Mathematics Subject Classification: 11K50 11K16 |
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