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Some Results On The Largest Partial Quotient In Continued Fractions

Author

Listed:
  • 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)

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.].

Suggested Citation

  • Lei Shang & Min Wu, 2022. "Some Results On The Largest Partial Quotient In Continued Fractions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-8, June.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:04:n:s0218348x22500955
    DOI: 10.1142/S0218348X22500955
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