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Starting with topological field theories we investigate the Ray-Singeranalytic torsion in three dimensions. For the lens Spaces L(p;q) an explicitanalytic continuation of the appropriate zeta functions is contructed andimplemented. Among the results obtained are closed formulae for the individualdeterminants involved, the large $p$ behaviour of the determinants and thetorsion, as well as an infinite set of distinct formulae for zeta(3): theordinary Riemann zeta function evaluated at s=3.  The torsion turns out to be trivial for the cases L(6,1), L((10,3) andL(12,5) and is, in general, greater than unity for large p and less than unityfor a finite number of p and q.

Ray-Singer Torsion, Topological Field Theories and the Riemann Zeta Function at s = 3