Abstract
The number of complex zeros of the Riemann zeta function with positive imaginary part less than is the sum of a “smooth” function and a “fluctuation.” Berry and Keating have shown that the asymptotic expansion of counts states of positive energy less than in a “regularized” semiclassical model with classical Hamiltonian . 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 .
- Received 27 May 2008
DOI:https://doi.org/10.1103/PhysRevLett.101.110201
©2008 American Physical Society
Synopsis
A Riemann calculator?
Published 15 September 2008
Calculus, group theory, and other mathematical tools are indispensable for understanding physics. Now the tables may be turned in a new approach toward solving a long-standing problem in mathematics.
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