IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i7p650-d250093.html
   My bibliography  Save this article

A Novel Integral Equation for the Riemann Zeta Function and Large t -Asymptotics

Author

Listed:
  • Konstantinos Kalimeris

    (Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK)

  • Athanassios S. Fokas

    (Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
    Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089-2560, USA)

Abstract

Based on the new approach to Lindelöf hypothesis recently introduced by one of the authors, we first derive a novel integral equation for the square of the absolute value of the Riemann zeta function. Then, we introduce the machinery needed to obtain an estimate for the solution of this equation. This approach suggests a substantial improvement of the current large t - asymptotics estimate for ζ 1 2 + i t .

Suggested Citation

  • Konstantinos Kalimeris & Athanassios S. Fokas, 2019. "A Novel Integral Equation for the Riemann Zeta Function and Large t -Asymptotics," Mathematics, MDPI, vol. 7(7), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:650-:d:250093
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/7/650/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/7/650/
    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:7:y:2019:i:7:p:650-:d:250093. 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.