On the Quantum Reconstruction of the Riemann zeros
| dc.creator | Sierra, German | |
| dc.date | 2007-11-07 | |
| dc.date.accessioned | 2026-07-07T11:38:36Z | |
| dc.date.available | 2026-07-07T11:38:36Z | |
| dc.description | We discuss a possible spectral realization of the Riemann zeros based on the Hamiltonian $H = xp$ perturbed by a term that depends on two potentials, which are related to the Berry-Keating semiclassical constraints. We find perturbatively the potentials whose Jost function is given by the zeta function $ζ(σ- i t)$ for $σ> 1$. For $σ= 1/2$ we find the potentials that yield the smooth approximation to the zeros. We show that the existence of potentials realizing the zeta function at $σ= 1/2$, as a Jost function, would imply that the Riemann zeros are point like spectrum embedded in the continuum, resolving in that way the emission/spectral interpretation. | |
| dc.description | 26 pages, 5 figures, to appear in the Proceedings of the ``5th International Symposium on Quantum Theory and Symmetries'' held at University of Valladolid, Spain, 2007 | |
| dc.identifier | https://arxiv.org/abs/0711.1063 | |
| dc.identifier | http://arxiv.org/abs/0711.1063 | |
| dc.identifier | J.Phys.A41:304041,2008 | |
| dc.identifier | doi:10.1088/1751-8113/41/30/304041 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/199622 | |
| dc.subject | Mathematical Physics | |
| dc.title | On the Quantum Reconstruction of the Riemann zeros | |
| dc.type | text |