IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i12p2042-d837391.html
   My bibliography  Save this article

A Generalized Bohr–Jessen Type Theorem for the Epstein Zeta-Function

Author

Listed:
  • Antanas Laurinčikas

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

  • Renata Macaitienė

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

Abstract

Let Q be a positive defined n × n matrix and Q [ x ̲ ] = x ̲ T Q x ̲ . The Epstein zeta-function ζ ( s ; Q ) , s = σ + i t , is defined, for σ > n 2 , by the series ζ ( s ; Q ) = ∑ x ̲ ∈ Z n \ { 0 ̲ } ( Q [ x ̲ ] ) − s , and is meromorphically continued on the whole complex plane. Suppose that n ⩾ 4 is even and φ ( t ) is a differentiable function with a monotonic derivative. In the paper, it is proved that 1 T meas t ∈ [ 0 , T ] : ζ ( σ + i φ ( t ) ; Q ) ∈ A , A ∈ B ( C ) , converges weakly to an explicitly given probability measure on ( C , B ( C ) ) as T → ∞ .

Suggested Citation

  • Antanas Laurinčikas & Renata Macaitienė, 2022. "A Generalized Bohr–Jessen Type Theorem for the Epstein Zeta-Function," Mathematics, MDPI, vol. 10(12), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2042-:d:837391
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/12/2042/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/12/2042/
    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:10:y:2022:i:12:p:2042-:d:837391. 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.