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

Charles Nash, D. J. O'Connor
1993 NATO ASI Series  
Starting with topological field theories we investigate the Ray-Singer analytic torsion in three dimensions. For the lens Spaces L(p; q) an explicit analytic continuation of the appropriate zeta functions is contructed and implemented. Among the results obtained are closed formulae for the individual determinants involved, the large p behaviour of the determinants and the torsion, as well as an infinite set of distinct formulae for ζ(3): the ordinary Riemann zeta function evaluated at s = 3.
more » ... torsion turns out to be trivial for the cases L(6, 1), L((10, 3) and L(12, 5) and is, in general, greater than unity for large p and less than unity for a finite number of p and q.
doi:10.1007/978-1-4899-1612-9_25 fatcat:urijbglqcvfzvadjzexdsu3544