  We connect two different approaches for calculating functional determinants
on quotients of hyperbolic spacetime: the heat kernel method and the
quasinormal mode method. For the example of a rotating BTZ background, we show
how the image sum in the heat kernel method builds up the logarithms in the
quasinormal mode method, while the thermal sum in the quasinormal mode method
builds up the integrand of the heat kernel. More formally, we demonstrate how
the heat kernel and quasinormal mode methods are linked via the Selberg zeta
function. We show that a 1-loop partition function computed using the heat
kernel method may be cast as a Selberg zeta function whose zeros encode
quasinormal modes. We discuss how our work may be used to predict quasinormal
modes on more complicated spacetimes.
