  We compute the full asymptotic expansion of the heat kernel
Trace$(\exp(-tD^2))$ where $D$ is, assuming RH, the self-adjoint operator whose
spectrum is formed of the imaginary parts of non-trivial zeros of the Riemann
zeta function. The coefficients of the expansion are explicit expressions
involving Bernoulli and Euler numbers. We relate the divergent terms with the
heat kernel expansion of the Dirac square root of the prolate wave operator
investigated in our joint work with Henri Moscovici.
