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The Phase of the Riemann Zeta Function and the Inverted Harmonic Oscillator

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arxiv chao-dyn/9406006 v1 pith:WAJFN3OD submitted 1994-06-16 chao-dyn hep-thnlin.CD

R.K. Bhaduri(Department of Physics , Astronomy , McMaster University , Hamilton , Ontario , Canada L8S 4M1) , Avinash Khare(Institute of Physics , Sachivalaya Marg
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Bhubaneswar-751 005 India.) J. Law( Guelph Waterloo Program for Graduate Work in Physics Physics Department University of Guelph Guelph Ont N1G 2W1)
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classification chao-dynhep-thnlin.CD
keywords functionzetazerosdiagraminvertedoscillatorphaseriemann
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The Argand diagram is used to display some characteristics of the Riemann Zeta function. The zeros of the Zeta function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram. This leads to the analogy with the scattering amplitude, and an approximate rule for the location of the zeros. The smooth phase of the Zeta function along the line of the zeros is related to the quantum density of states of an inverted oscillator.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Equivalent Hamiltonian approach to quantum cosmology of integrable models

    gr-qc 2019-08 conditional novelty 5.0 of 10

    For two integrable minisuperspace cosmologies, the paper constructs equivalent Hamiltonians via Faddeev-Jackiw reduction and uses them to study quantum wave packets and Wigner functions.

  2. The Saddle Point of Everything

    physics.gen-ph 2026-05 unverdicted novelty 3.0 of 10

    The inverted harmonic oscillator and its dual are argued to underpin a unique unitary renormalizable quantum gravity in four dimensions, yielding a non-singular universe and Starobinsky inflation.

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