IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i22p4615-d1278086.html
   My bibliography  Save this article

Gram Points in the Universality of the Dirichlet Series with Periodic Coefficients

Author

Listed:
  • Darius Šiaučiūnas

    (Institute of Regional Development, Šiauliai Academy, Vilnius University, Vytauto Str. 84, LT-76352 Šiauliai, Lithuania
    These authors contributed equally to this work.)

  • Monika Tekorė

    (Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

Abstract

Let a = { a m : m ∈ N } be a periodic multiplicative sequence of complex numbers and L ( s ; a ) , s = σ + i t a Dirichlet series with coefficients a m . In the paper, we obtain a theorem on the approximation of non-vanishing analytic functions defined in the strip 1 / 2 < σ < 1 via discrete shifts L ( s + i h t k ; a ) , h > 0 , k ∈ N , where { t k : k ∈ N } is the sequence of Gram points. We prove that the set of such shifts approximating a given analytic function is infinite. This result extends and covers that of [Korolev, M.; Laurinčikas, A. A new application of the Gram points. Aequat. Math. 2019 , 93 , 859–873]. For the proof, a limit theorem on weakly convergent probability measures in the space of analytic functions is applied.

Suggested Citation

  • Darius Šiaučiūnas & Monika Tekorė, 2023. "Gram Points in the Universality of the Dirichlet Series with Periodic Coefficients," Mathematics, MDPI, vol. 11(22), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4615-:d:1278086
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/22/4615/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/22/4615/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:11:y:2023:i:22:p:4615-:d:1278086. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.