
Physics 2007
On the Quantum Reconstruction of the Riemann zerosDOI: 10.1088/17518113/41/30/304041 Abstract: 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 BerryKeating semiclassical constraints. We find perturbatively the potentials whose Jost function is given by the zeta function $\zeta(\sigma  i t)$ for $\sigma > 1$. For $\sigma = 1/2$ we find the potentials that yield the smooth approximation to the zeros. We show that the existence of potentials realizing the zeta function at $\sigma = 1/2$, 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.
