  After a brief survey of zeta function regularization issues and of the
related multiplicative anomaly, illustrated with a couple of basic examples,
namely the harmonic oscillator and quantum field theory at finite temperature,
an application of these methods to the computation of functional determinants
corresponding to massive Laplacians on spheres in arbitrary dimensions is
presented. Explicit formulas are provided for the Laplace operator on spheres
in $N=1,2,3,4$ dimensions and for `vector' and `tensor' Laplacians on the
unitary sphere $S^4$.
