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Metric Theory Of Partial Quotients Of N-Continued Fractions

Author

Listed:
  • JINFENG WANG

    (School of Mathematics and Statistics, Huazhong University of Science and Technology, 430074 Wuhan, P. R. China)

  • YUAN ZHANG

    (Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Benbu 233030, P. R. China)

Abstract

On analogy of the regular continued fractions, for any fixed positive integer N ∈ ℕ, every x ∈ [0, 1) can be expanded into an N-continued fraction, denoted by x = [a1(x),a2(x),…]N, where an(x) are called the partial quotients. In this paper, we concern the metric theory of the partial quotients. More precisely, let ϕ: ℕ → (0,∞), the Borel–Bernstein theorem and Hausdorff dimension of the set {x ∈ [0, 1): an(x) ≥ ϕ(n) for infinitely many n ∈ ℕ} are determined. This generalizes the results of regular continued fractions.

Suggested Citation

  • Jinfeng Wang & Yuan Zhang, 2022. "Metric Theory Of Partial Quotients Of N-Continued Fractions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-16, February.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22500220
    DOI: 10.1142/S0218348X22500220
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