components of this expression both for their usefulness in their own right and to verify that the combined result agrees with the Ray-Singer torsion. We do this in the restricted setting where $M$ belongs to a class of three dimensional lens spaces. In the next section we specify the lens spaces that we work with and obtain the eigenvalues and their degeneracies of the Laplacians on these spaces. We now want to turn to field theories defined on lens spaces—for general background on lens spaces cf. \[3,4\] and references therein—briefly, a lens space can be constructed as follows: Take an odd dimensional sphere $S^{2n+1}$, considered as a subset of ${\bf C}^n$, on which a finite cyclic group of rotations $G$, say, acts. The quotient $S^{2n+1}/G$ of the sphere under this action is a lens space. More precisely, suppose that $G$ is of order $p$, $(z_1,\ldots,z_n)\in {\bf C}^n$ and the group action takes the form $$\eqalign{{}&(z_1,\ldots,z_n)\longmapsto (\exp(2\pi i q_1/p)z_1,\ldots,
\exp(2\pi i q_n/p)z_n)\cr
{}&\hbox{with }q_1,\dots,q_n\quad\hbox{integers relatively prime to }p\cr}
\no$$ then the quotient $S^{2n+1}/G$ is a lens space often denoted by $L(p;q_1,\dots,q_n)$. A formula for the torsion of these spaces was first worked out by Ray \[2\]. To our knowledge however there 