  We develop a unified method to study spectral determinants for several
different manifolds, including spheres and hemispheres, and projective spaces.
This is a direct consequence of an approach based on deriving recursion
relations for the corresponding zeta functions, which we are then able to solve
explicitly. Apart from new applications such as hemispheres, we also believe
that the resulting formulae in the cases for which expressions for the
determinant were already known are simpler and easier to compute in general,
when compared to those resulting from other approaches.
