The H=xp model revisited and the Riemann zeros

Understand

Berry and Keating conjectured that the classical Hamiltonian H = xp is related to the Riemann zeros.

• A regularization of this model yields semiclassical energies that behave, in average, as the non trivial zeros of the Riemann zeta function.
• However, the classical trajectories are not closed, rendering the model incomplete.
• In this paper, we show that the Hamiltonian H = x (p + l_p^2/p) contains closed periodic orbits, and that its spectrum coincides with the average Riemann zeros.