IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v55y2024i3d10.1007_s13226-024-00650-z.html
   My bibliography  Save this article

Divisibility of integer laurent polynomials, homoclinic points, and lacunary independence

Author

Listed:
  • Douglas Lind

    (University of Washington)

  • Klaus Schmidt

    (University of Vienna)

Abstract

Let f, p, and q be Laurent polynomials with integer coefficients in one or several variables, and suppose that f divides $$p+q$$ p + q . We establish sufficient conditions to guarantee that f individually divides p and q. These conditions involve a bound on coefficients, a separation between the supports of p and q, and, surprisingly, a requirement on the complex variety of f called atorality satisfied by many but not all polynomials. Our proof involves a related dynamical system and the fundamental dynamical notion of homoclinic point. Without the atorality assumption our methods fail, and it is unknown whether our results hold without this assumption. We use this to establish exponential recurrence of the related dynamical system, and conclude with some remarks and open problems.

Suggested Citation

  • Douglas Lind & Klaus Schmidt, 2024. "Divisibility of integer laurent polynomials, homoclinic points, and lacunary independence," Indian Journal of Pure and Applied Mathematics, Springer, vol. 55(3), pages 1089-1095, September.
    • Handle: RePEc:spr:indpam:v:55:y:2024:i:3:d:10.1007_s13226-024-00650-z
    DOI: 10.1007/s13226-024-00650-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-024-00650-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13226-024-00650-z?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:spr:indpam:v:55:y:2024:i:3:d:10.1007_s13226-024-00650-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.