Regularized and $L^2$-Determinants

Details Regularized and $L^2$-Determinants Regularized and $L^2$-Determinants

1995-11-23

arxiv.org/abs/dg-ga/9511009v2

Proc. London Math. Soc.

Mathematics

Differential Geometry

LATEX, 30 pages

Scientific paper

It is shown that in a tower of coverings the regularized determinant of a generalized Laplacian converges to the $L^2$-determinant. This shows generic nontriviality of analytic torsion or regularized determinants since the $L^2$-counterparts are easier to compute. We further have an "Euler product expansion" for regularized determinants in terms of equivariant $L^2$-determinants.

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