Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-12-03
J.Math.Phys. 36 (1995) 1462-1505; Erratum-ibid. 36 (1995) 4549
Physics
High Energy Physics
High Energy Physics - Theory
49 pages
Scientific paper
10.1063/1.531134
We obtain explicit expressions for the determinants of the Laplacians on zero and 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 these lens spaces. As a consequence we obtain an infinite class of formulae for the Riemann zeta function $\zeta(3)$. The value of these determinants (and the torsion) grows as the size of the fundamental group of the lens space increases and this is also computed. The triviality of the torsion for just the three lens spaces $L(6,1)$, $L(10,3)$ and $L(12,5)$ is also noted. (postscript figures available as a compressed tar file)
Connor Denjoe O'
Nash Charles
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