Wikipedia article Hilbert-Polya conjecture has a link to an article H=xp and the Riemann zeros by Berry & Keating. They mention that the number of energy levels below given [itex]E[/itex] could be counted by computing the area enclosed by the contour [itex]H(x,p)=E[/itex] in the phase space. What is that all about? Does there exist some theorem concerning this? Can it be justified easily? What information sources are there about this?