  According to a conjecture attributed to Polya and Hilbert, there is a
self-adjoint operator whose eigenvalues are the the nontrivial zeros of the
Riemann zeta function. We show that the near-horizon dynamics of a massive
scalar field in the Schwarzscild black hole spacetime, under a reasonable
boundary condition, gives rise to normal mode frequencies that coincide with
the nontrivial Riemann zeros. In achieving this result, we exploit the
Bekenstein conjecture of black hole area quantization, and argue that it is
responsible for the breaking of the continuous scale symmetry of the near
horizon dynamics into a discrete one.
