  We continue the study of a special entry in the AdS/CFT dictionary, namely a
holographic formula relating the functional determinant of the scattering
operator in an asymptotically locally anti-de Sitter (ALAdS) space to a
relative functional determinant of the scalar Laplacian in the bulk. A
heuristic derivation of the formula involves a one-loop quantum effect in the
bulk and the corresponding sub-leading correction at large N on the boundary.
  We presently explore a higher-dimensional version of the spinning BTZ black
hole obtained as a quotient of hyperbolic space by a discrete subgroup of
isometries generated by a loxodromic (or hyperbolic) element consisting of
dilation (temperature) and torsion angles (spinning). The bulk computation is
done using heat-kernel techniques and fractional calculus. At the boundary, we
get a recursive scheme that allows us to range from the non-spinning to the
full-fledged spinning geometries. The determinants are compactly expressed in
terms of an associated (Patterson-)Selberg zeta function and a connection to
quasi-normal frequencies is discussed.
