  The Selberg zeta function and trace formula are powerful tools used to
calculate kinetic operator spectra and quasinormal modes on hyperbolic quotient
spacetimes. In this article, we extend this formalism to non-hyperbolic
quotients by constructing a Selberg zeta function for warped AdS$_3$ black
holes. We also consider the so-called self-dual solutions, which are of
interest in connection to near-horizon extremal Kerr. We establish a map
between the zeta function zeroes and the quasinormal modes on warped AdS$_3$
black hole backgrounds. In the process, we use a method involving conformal
coordinates and the symmetry structure of the scalar Laplacian to construct a
warped version of the hyperbolic half-space metric, which to our knowledge is
new and may have interesting applications of its own, which we describe. We end
by discussing several future directions for this work, such as computing 1-loop
determinants (which govern quantum corrections) on the quotient spacetimes we
consider, as well as adapting the formalism presented here to more generic
orbifolds.
