Abstract
German Sierra (UAM-CSIC)
On the spectral interpretation of the Riemann zeros
It has been long conjectured that the imaginary part of the non trivial zeros of the Riemann zeta function are the eigenvalues of a self-adjoint operator acting in a Hilbert space. In 1999 this idea was put on a more concrete ground by Berry, Keating and Connes who suggested, using semiclassical arguments, that this operator could be related to the one dimensional Hamiltonian H = xp. In this talk we shall show that this simple Hamiltonian gives the dynamics of a charged particle moving in two dimensions and subject to the action of a magnetic and electric field. The quantization of this model helps to clarify some issues concerning the different spectral interpretation of the Riemann zeros and may shed new light about the Riemann Hamiltonian.