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Title: Landau levels and Riemann zeros
Authors: Sierra, Germán, Townsend, Paul K.
Keywords: Mathematical Physics
Mesoscopic Systems and Quantum Hall Effect
High Energy Physics - Theory
Number Theory
Quantum Physics
[PACS] Algebraic structures and number theory
[PACS] Quantum chaos; semiclassical methods
Issue Date: 12-Sep-2008
Publisher: American Physical Society
Series/Report no.: IFT-UAM/CSIC 08-26
Abstract: The number N(E) of complex zeros of the Riemann zeta function with positive imaginary part less than E is the sum of a `smooth' function Ñ(E) and a 'fluctuation'. Berry and Keating have shown that the asymptotic expansion of Ñ(E) counts states of positive energy less than E in a 'regularized' semi-classical model with classical Hamiltonian H=xp. For a different regularization, Connes has shown that it counts states 'missing' from a continuum. Here we show how the 'absorption spectrum' model of Connes emerges as the lowest Landau level limit of a specific quantum mechanical model for a charged particle on a planar surface in an electric potential and uniform magnetic field. We suggest a role for the higher Landau levels in the fluctuation part of N(E).
Description: 4 pages, 2 figures.-- PACS numbers: 02.10.De, 05.45.Mt.-- ArXiv pre-print available at:
Publisher version (URL):
ISSN: 0031-9007
???metadata.dc.identifier.doi???: 10.1103/PhysRevLett.101.110201
Citation: Physical Review Letters 101(11): 110201 (2008)
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