Landau levels and Riemann zeros

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dc.creatorSierra, German
dc.creatorTownsend, Paul K.
dc.date2008-05-27
dc.date2008-09-22
dc.date.accessioned2026-07-07T11:44:47Z
dc.date.available2026-07-07T11:44:47Z
dc.descriptionThe 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 $\bar N(E)$ and a `fluctuation'. Berry and Keating have shown that the asymptotic expansion of $\bar N(E)$ 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 $N(E)$.
dc.description4 pages, 2 figures, minor corrections added
dc.identifierhttps://arxiv.org/abs/0805.4079
dc.identifierhttp://arxiv.org/abs/0805.4079
dc.identifierPhys.Rev.Lett.101:110201,2008
dc.identifierdoi:10.1103/PhysRevLett.101.110201
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/201677
dc.subjectMathematical Physics
dc.subjectMesoscale and Nanoscale Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectNumber Theory
dc.subjectQuantum Physics
dc.titleLandau levels and Riemann zeros
dc.typetext

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