Regularized and $L^2$-Determinants

Anton Deitmar

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arXiv · dg-ga/9511009

Regularized and $L^2$-Determinants

Anton Deitmar

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Abstract

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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Anton Deitmar. 1996-03-18. Regularized and $L^2$-Determinants. https://arxiv.org/abs/dg-ga/9511009

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