is no computation of the individual determinants of Laplacians on these spaces in the literature. Since these are of independent field theoretic significance and from these the torsion is constructed it is instructive to examine these separately and construct the torsion from them. This we will proceed to do in the next sections focusing on the situation that obtains when $n=2$ and $G$ is the group ${\bf Z}_p\equiv {\bf Z}/p{\bf Z}$. For simplicity we shall denote the resulting lens space $S^3/{\bf Z}_p=L(p;1,1)$ by $L(p)$, we shall also denote the lens space $L(p,1,q)$ by $L(p,q)$; in passing we note that when $p=2$ we have $L(2)={\bf R}P^3\simeq SO(3)$.

The group action above defines a representation $V$, say, of $\pi_1(L(p))$ and also determines a flat bundle $F=(V\times S^3)/Z_p$, over $L(p)$. It is the determinants of Laplacians and the resulting torsion of this $F$ over $L(p)$ with which we are concerned here. Using zeta functions the torsion of these lens spaces is therefore given by $$\ln T(L(p),F)=-\sum_0^3(-1)^qq\left.{d\zeta_{\Delta_q^{F}}(s)\over
ds}\right\vert_{s=0}\no$$

As an aid to the calculation of $\ln T(L(p),F)$ it is useful to introduce the notation $$\eqalign{\tau(p,s)&=-\sum_0^3(-1)^qq\zeta_{\Delta_q^{F}}(s)\cr
                 T(p)&=T(L(p),F)\cr}$$ The relationship between the two functions being clearly $$\ln T(p)=\left.{d \tau(p,s) \over ds}\right\vert_{s=0}\no$$ For $\tau(p,s)$ itself we now 