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We relate the heat kernel and quasinormal mode methods of computing the1-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 andWilliams showed for a scalar field that the zeros of the Selberg zeta functioncoincide with the poles of the associated scattering operator upon a relabelingof integers. We extend the integer relabeling to the case of general spin, anddiscuss its relationship to the removal of non-square-integrable Euclidean zeromodes.

BTZ one-loop determinants via the Selberg zeta function for general spin