  We relate the heat kernel and quasinormal mode methods of computing the
1-loop partition function of arbitrary spin fields on a rotating (Euclidean)
BTZ background using the Selberg zeta function associated with
$\mathbb{H}^{3}/\mathbb{Z}$, extending (1811.08433). Previously, Perry and
Williams showed for a scalar field that the zeros of the Selberg zeta function
coincide with the poles of the associated scattering operator upon a relabeling
of integers. We extend the integer relabeling to the case of general spin, and
discuss its relationship to the removal of non-square-integrable Euclidean zero
modes.
