We investigate the propagation of arbitrarily coupled scalar fields on the
N-dimensional hyperbolic space H-N. Using the zeta-function regularization
we compute exactly the one-loop effective action. The vacuum expectation va
lue of quadratic field fluctuations and the one-loop renormalized stress te
nsor are then computed using the recently proposed direct zeta-function tec
hnique. Our computation tests the validity of this approach in the presence
of a continuous spectrum. Our results apply as well to the N-dimensional a
nti-de Sitter space-time, whose appropriate euclidean section is the hyperb
olic space H-N. (C) 1999 Elsevier Science B.V. All rights reserved.