  We investigate the late-time tail of the retarded Green function for the
dynamics of a linear field perturbation of Kerr spacetime. We develop an
analytical formalism for obtaining the late-time tail up to arbitrary order for
general integer spin of the field. We then apply this formalism to obtain the
details of the first five orders in the late-time tail of the Green function
for the case of a scalar field: to leading order we recover the known power law
tail $t^{-2\ell-3}$, and at third order we obtain a logarithmic correction,
$t^{-2\ell-5}\ln t$, where $\ell$ is the field multipole.
