1994/06/16 by R. K. Bhaduri, Avinash Khare, J. Law · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Protein Structure and Dynamics #Quantum chaos and dynamical systems #chao-dyn #hep-th #nlin.CD
paper · pdf · doi:10.1103/physreve.52.486
published as Phys.Rev. E52 (1995) 486 · 4 pages of postscript file with embeded figures, in uuencoded tar format
arxiv created 1994/06/16 · openalex publication_date 1995/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The Argand diagram is used to display some characteristics of the Riemann \ensuremathζ function. The zeros of the \ensuremathζ function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram. The behavior of the phase of the \ensuremathζ function on and off the line of zeros is studied. Up to some distance from the line of the complex zeros, the phase angle is shown to still retain their memory. The Argand plots also lead to an analogy with the scattering amplitude and an approximate rule for the location of the zeros. The smooth phase of the \ensuremathζ function along the line of the zeros is related to the quantum density of states of an inverted oscillator.