to do this is to take $M$ to be the quotient of a sphere $S^n$ by a finite cyclic group $G$. This quotient $S^n/G$, described in more detail below, is what is called a lens space, written as $L(p,q)$. In this paper we take $M$ to be a lens space on which is placed a topological field theory whose classical phase space consists of flat connections.

Our approach is to take the model given by the field theory and analyse it in detail on a whole infinite class of lens spaces. We work in three dimensions and realise $M$ as the quotient of the manifold $S^3$ by the action of a discrete group $Z_{p}$. The resulting partition function on this manifold is a combinatorial invariant of the manifold known as the Ray-Singer torsion of the manifold. However the field theory gives this partition function as the ratio of a set of determinants. A standard technique in field theory has been to define these functional determinants through the analytic continuation of the zeta functions of the associated operators.

In this work we investigate the individual determinants that arise and obtain highly explicit expressions for them. Our expressions have an intriguing structure 