IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v29y2021i07ns0218348x21502200.html
   My bibliography  Save this article

On The Fast Increasing Digits In Lãœroth Expansions

Author

Listed:
  • MEIYING LÃœ

    (School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P. R. China)

  • JING XIE

    (School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P. R. China)

Abstract

For any x ∈ (0, 1], let x = 1 d1 + 1 d1(d1 − 1)d2 + ⋯ + 1 d1(d1 − 1)⋯dn−1(dn−1 − 1)dn + ⋯ be its Lüroth expansion with digits {dj ≥ 2,j ≥ 1}. Let ψ : ℕ → ℠+ be a function satisfying ψ(n)/n →∞ as n →∞ and E(ψ) := x ∈ (0, 1] :limn→∞ 1 ψ(n)∑j=1nlog d j(x) = 1 . In this paper, we give the Hausdorff dimension of the set E(ψ) without any extra condition on ψ. This result extends the former work of the first author (Fractals 28(4) (2020) 2050064, doi:10.1142/S0218348X20500644).

Suggested Citation

  • Meiying L㜠& Jing Xie, 2021. "On The Fast Increasing Digits In Lãœroth Expansions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-7, November.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:07:n:s0218348x21502200
    DOI: 10.1142/S0218348X21502200
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X21502200
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X21502200?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:fracta:v:29:y:2021:i:07:n:s0218348x21502200. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.