IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i4p917-d1065297.html
   My bibliography  Save this article

Unified Theory of Zeta-Functions Allied to Epstein Zeta-Functions and Associated with Maass Forms

Author

Listed:
  • Nianliang Wang

    (College of Applied Mathematics and Computer Science, Shangluo University, Shangluo 726000, China
    Zum Professor Dr. Christopher Deninger für seinen 65sten Geburztag gewidmet mit freunlichen Grüssen und gründlichen Respekt.
    These authors contributed equally to this work.)

  • Takako Kuzumaki

    (Faculty of Engineering, Gifu University, Gifu 501-1193, Japan
    Zum Professor Dr. Christopher Deninger für seinen 65sten Geburztag gewidmet mit freunlichen Grüssen und gründlichen Respekt.
    These authors contributed equally to this work.)

  • Shigeru Kanemitsu

    (KSCSTE-Kerala School of Mathematics, Kunnamangalam, Kozhikode 673571, Kerala, India
    Zum Professor Dr. Christopher Deninger für seinen 65sten Geburztag gewidmet mit freunlichen Grüssen und gründlichen Respekt.
    These authors contributed equally to this work.)

Abstract

In this paper, we shall establish a hierarchy of functional equations (as a G -function hierarchy) by unifying zeta-functions that satisfy the Hecke functional equation and those corresponding to Maass forms in the framework of the ramified functional equation with (essentially) two gamma factors through the Fourier–Whittaker expansion. This unifies the theory of Epstein zeta-functions and zeta-functions associated to Maass forms and in a sense gives a method of construction of Maass forms. In the long term, this is a remote consequence of generalizing to an arithmetic progression through perturbed Dirichlet series.

Suggested Citation

  • Nianliang Wang & Takako Kuzumaki & Shigeru Kanemitsu, 2023. "Unified Theory of Zeta-Functions Allied to Epstein Zeta-Functions and Associated with Maass Forms," Mathematics, MDPI, vol. 11(4), pages 1-24, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:917-:d:1065297
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/4/917/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/4/917/
    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:4:p:917-:d:1065297. 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.