  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.
