Functional Determinant of the Massive Laplace Operator and the   Multiplicative Anomaly
  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 $S^4$. 
G. Cognola, E. Elizalde and S. Zerbini
hep-th math-ph math.MP