SOME RESULTS ON THE LARGEST PARTIAL QUOTIENT IN CONTINUED FRACTIONS

Lei Shang and Min Wu ()
Additional contact information
Lei Shang: School of Mathematics, Sun Yat-sen University, Guangzhou 510275, P. R. China
Min Wu: School of Mathematics, South China, University of Technology, Guangzhou 510640, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 04, 1-8

Abstract: Let ψ : ℕ → ℠+ be a function satisfying ψ(n) →∞ as n →∞. Write E(ψ) := x ∈ (0, 1) :limn→∞Tn(x) ψ(n) = 1 , where Tn(x) denotes the largest partial quotient among the first n terms in the continued fraction expansion of x. We prove that E(ψ) has full Hausdorff dimension for a large class of functions ψ, which strengthens the result of [L. Fang and J. Liu, On the largest partial quotients in continued fraction expansions, Fractals 29 (2021) 2150099.].

Keywords: Continued Fractions; Largest Partial Quotient; Growth Rate; Hausdorff Dimension (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X22500955
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:30:y:2022:i:04:n:s0218348x22500955

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X22500955

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().