Abstract
The Hilbert-Pólya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum Hamiltonian. If so, conjectures by Katz and Sarnak put this Hamiltonian in the Altland-Zirnbauer universality class . This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of . This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros.
- Received 12 May 2011
DOI:https://doi.org/10.1103/PhysRevLett.107.100201
© 2011 American Physical Society