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We obtain explicit expressions for the determinants of the Laplacians on zeroand one forms for an infinite class of three dimensional lens spaces $L(p,q)$.These expressions can be combined to obtain the Ray-Singer torsion of theselens spaces. As a consequence we obtain an infinite class of formulae for theRiemann zeta function $\zeta(3)$. The value of these determinants (and thetorsion) grows as the size of the fundamental group of the lens space increasesand this is also computed. The triviality of the torsion for just the threelens spaces $L(6,1)$, $L(10,3)$ and $L(12,5)$ is also noted. (postscriptfigures available as a compressed tar file)Comment: 49 page

Determinants of Laplacians, the Ray–Singer torsion on lens spaces and the Riemann zeta function