of their own For example, on the lens space $L(2,1)$, we find that $$\eqalign{\ln\Det d^*d_{0}&=-{3\zeta(3)\over2\pi^2}+\ln2\cr
\ln\Det d^*d_1&=-{3\zeta(3)\over\pi^2}-2\ln2\cr}\no$$ Similar, though more complicated, expressions occur for each of the lens spaces $L(p,1)$ for $p=3,4,\dots$. This in turn leads to non-trivial formulae for $\zeta(3)$: to give two examples we find that $$\eqalign{\zeta(3)&={2\pi^2\over7}\ln(2)
-{8\over7}\int_0^{\pi/2}dz\,z^2\cot(z)\cr
\zeta(3)&={2\pi^2\over13}\ln 3
-{9\over 13}\int_{0}^{\pi\over3}dz\,z(z+{\pi\over3})\cot(z)
-{9\over 13}\int_{0}^{2\pi\over3}dz\,z(z-{\pi\over3})\cot(z)
\cr}\no$$ these being the formulae that come from $L(2,1)$ and $L(3,1)$ respectively.

The structure of the paper is as follows. In Section 2 we describe the topological field theory under consideration. In section 3 we define the Ray-Singer torsion and describe the lens spaces with which we work; we also carry out the non-trivial task of obtaining the eigenvalues and degeneracies for the Laplacians on $p$-forms acting on these spaces. Section 4 deals with the lens space $L(2,1)$ ($SO(3)$) and is a construction of the analytic continuation of the appropriate $p$-form zeta functions followed by a calculation of their associated determinants. Sections 5 and 6 describe the analogous calculation and expressions for the infinite classes of manifolds corresponding to $L(p,1)$ for $p$ odd and even respectively. Finally in section 7 we present our conclusions, some comments on the torsion of $L(p,q)$ for general $q$, 