  We propose a method of computing one-loop determinants in black hole
spacetimes (with emphasis on asymptotically anti-de Sitter black holes) that
may be used for numerics when completely-analytic results are unattainable. The
method utilizes the expression for one-loop determinants in terms of
quasinormal frequencies determined by Denef, Hartnoll and Sachdev in
\cite{Denef:2009kn}. A numerical evaluation must face the fact that the sum
over the quasinormal modes, indexed by momentum and overtone numbers, is
divergent. A necessary ingredient is then a regularization scheme to handle the
divergent contributions of individual fixed-momentum sectors to the partition
function. To this end, we formulate an effective two-dimensional problem in
which a natural refinement of standard heat kernel techniques can be used to
account for contributions to the partition function at fixed momentum. We test
our method in a concrete case by reproducing the scalar one-loop determinant in
the BTZ black hole background. We then discuss the application of such
techniques to more complicated spacetimes.
