Ray-Singer Torsion, Topological field theories and the Riemann zeta function at s = 3

Nash, Charles and O'Connor, Denjoe (1992) Ray-Singer Torsion, Topological field theories and the Riemann zeta function at s = 3. (Preprint)

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Abstract

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 constructed 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. The 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.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 14:13
Last Modified: 19 Jul 2018 10:50
URI: http://dair.dias.ie/id/eprint/740

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