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Slow increasing functions and the largest partial quotients in continued fraction expansions
| Content Provider | Scilit |
|---|---|
| Author | Chang, Jinhua Chen, Haibo |
| Copyright Year | 2016 |
| Description | Let 0 ⩽ α ⩽ ∞ and ψ be a positive function defined on (0, ∞). In this paper, we will study the level sets L(α, {ψ(n)}), B(α, {ψ(n)}) and T(α, {ψ(n)}) which are related respectively to the sequence of the largest digits among the first n partial quotients ${L_{n}(x)}_{n≥1}$, the increasing sequence of the largest partial quotients ${B_{n}(x)}_{n⩾1}$ and the sequence of successive occurrences of the largest partial quotients ${T_{n}(x)}_{n⩾1}$ in the continued fraction expansion of x ∈ [0,1) ∩ $ℚ^{c}$. Under suitable assumptions of the function ψ, we will prove that the sets L(α, {ψ(n)}), B(α, {ψ(n)}) and T(α, {ψ(n)}) are all of full Hausdorff dimensions for any 0 ⩽ α ⩽ ∞. These results complement some limit theorems given by J. Galambos [4] and D. Barbolosi and C. Faivre [1]. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7B2F93D9908EF77AA8BC8C7FA33F0232/S0305004116000815a.pdf/div-class-title-slow-increasing-functions-and-the-largest-partial-quotients-in-continued-fraction-expansions-div.pdf |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004116000815 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 1 |
| Volume Number | 164 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2018-01-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society Continued Fraction Fraction Expansions Largest Partial Partial Quotients |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
