Research Commons
      • Browse 
        • Communities & Collections
        • Titles
        • Authors
        • By Issue Date
        • Subjects
        • Types
        • Series
      • Help 
        • About
        • Collection Policy
        • OA Mandate Guidelines
        • Guidelines FAQ
        • Contact Us
      • My Account 
        • Sign In
        • Register
      View Item 
      •   Research Commons
      • University of Waikato Research
      • Computing and Mathematical Sciences
      • Computing and Mathematical Sciences Papers
      • View Item
      •   Research Commons
      • University of Waikato Research
      • Computing and Mathematical Sciences
      • Computing and Mathematical Sciences Papers
      • View Item
      JavaScript is disabled for your browser. Some features of this site may not work without it.

      The holomorphic flow of the Riemann zeta function

      Broughan, Kevin A.; Barnett, A. Ross
      Thumbnail
      Files
      AMS Broughan Riemann zeta.pdf
      788.5Kb
      DOI
       10.1090/S0025-5718-03-01529-1
      Find in your library  
      Citation
      Export citation
      Broughan, K.A. & Barnett, A.R.(2003). The holomorphic flow of the Riemann zeta function . Mathematics of Computation, 73, 987-1004.
      Permanent Research Commons link: https://hdl.handle.net/10289/1263
      Abstract
      The flow of the Riemann zeta function, ś = ς(s), is considered, and phase portraits are presented. Attention is given to the characterization of the flow lines in the neighborhood of the first 500 zeros on the critical line. All of these zeros are foci. The majority are sources, but in a small proportion of exceptional cases the zero is a sink. To produce these portraits, the zeta function was evaluated numerically to 12 decimal places, in the region of interest, using the Chebyshev method and using Mathematica.

      The phase diagrams suggest new analytic properties of zeta, of which some are proved and others are given in the form of conjectures.
      Date
      2003-11
      Type
      Journal Article
      Publisher
      American Mathematical Society
      Rights
      First published in Mathematics of Computation in volume 73, pages 987-1004, published by the American Mathematical Society. Copyright 2003, American Mathematical Society.
      Collections
      • Computing and Mathematical Sciences Papers [1441]
      Show full item record  

      Usage

      Downloads, last 12 months
      27
       
       
       

      Usage Statistics

      For this itemFor all of Research Commons

      The University of Waikato - Te Whare Wānanga o WaikatoFeedback and RequestsCopyright and Legal Statement