  In this note, we calculate the one-loop determinant for a massive scalar
(with conformal dimension $\Delta$) in even-dimensional AdS$_{d+1}$ space,
using the quasinormal mode method developed in arXiv:0908.2657 by Denef,
Hartnoll, and Sachdev. Working first in two dimensions on the related Euclidean
hyperbolic plane $H_2$, we find a series of zero modes for negative real values
of $\Delta$ whose presence indicates a series of poles in the one-loop
partition function $Z(\Delta)$ in the $\Delta$ complex plane; these poles
contribute temperature-independent terms to the thermal AdS partition function
computed in arXiv:0908.2657. Our results match those in a series of papers by
Camporesi and Higuchi, as well as Gopakumar et al. in arXiv:1103.3627 and
Banerjee et al. in arXiv:1005.3044. We additionally examine the meaning of
these zero modes, finding that they Wick-rotate to quasinormal modes of the
AdS$_2$ black hole. They are also interpretable as matrix elements of the
discrete series representations of $SO(2,1)$ in the space of smooth functions
on $S^1$. We generalize our results to general even dimensional AdS$_{2n}$,
again finding a series of zero modes which are related to discrete series
representations of $SO(2n,1)$, the motion group of $H_{2n}$.
