  Spectral functions relevant in the context of quantum field theory under the
influence of spherically symmetric external conditions are analysed. Examples
comprise heat-kernels, determinants and spectral sums needed for the analysis
of Casimir energies. First, we summarize that a convenient way of handling them
is to use the associated zeta function. A way to determine all its needed
properties is derived. Using the connection with the mentioned spectral
functions, we provide: i.) a method for the calculation of heat-kernel
coefficients of Laplace-like operators on Riemannian manifolds with smooth
boundaries and ii.) an analysis of vacuum energies in the presence of
spherically symmetric boundaries and external background potentials.
