Beta-expansion and continued fraction expansion |
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| Authors: | Bing Li |
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| Affiliation: | a Department of Mathematics, Wuhan University, Wuhan, Hubei 430072, PR China
b Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China |
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| Abstract: | For any real number β>1, let ε(1,β)=(ε1(1),ε2(1),…,εn(1),…) be the infinite β-expansion of 1. Define  . Let x∈[0,1) be an irrational number. We denote by kn(x) the exact number of partial quotients in the continued fraction expansion of x given by the first n digits in the β-expansion of x. If  is bounded, we obtain that for all x∈[0,1)?Q, |
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| Keywords: | β-Expansion Continued fraction expansion Lé vy constant |
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