IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v29y2021i06ns0218348x21501425.html
   My bibliography  Save this article

Exact Dimensions Of Exceptional Sets In Lãœroth Expansions

Author

Listed:
  • YAN FENG

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

  • BO TAN

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

  • QING-LONG ZHOU

    (��School of Science, Wuhan University of Technology, 430074 Wuhan, P. R. China)

Abstract

For x ∈ (0, 1], let x = [d1(x),d2(x),…,dn(x),…]L be its Lüroth expansion, and let {pn(x)/qn(x)}n≥1 be the sequence of convergents of x. Define the exceptional sets E(β) = x ∈ (0, 1]: limn→∞log dn+1(x) log qn(x) = β and U(β) = x ∈ (0, 1]: limsupn→∞log dn+1(x) log qn(x) = β. Arroyo and González Robert [Hausdorff dimension of sets of numbers with large Lüroth elements, preprint (2020), arXiv:2010.13932] presented upper and lower bound estimations for the Hausdorff dimension of E(β). In this paper, we determine the Hausdorff dimensions of the sets E(β) as well as U(β).

Suggested Citation

  • Yan Feng & Bo Tan & Qing-Long Zhou, 2021. "Exact Dimensions Of Exceptional Sets In Lãœroth Expansions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-13, September.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:06:n:s0218348x21501425
    DOI: 10.1142/S0218348X21501425
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X21501425
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X21501425?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:06:n:s0218348x21501425. 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.