1992/10/01 by Charles Nash, C. Nash, Denjoe O' Connor +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Black Holes and Theoretical Physics #Topological and Geometric Data Analysis #hep-th #math.DG
paper · pdf · doi:10.48550/arxiv.hep-th/9210005
10 pages
arxiv created 1992/10/01 · arxiv updated 2009/11/30
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 zeta(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.