Regularized determinants of the Laplacian for cofinite Kleinian groups with finite-dimensional unitary representations

Details Regularized determinants of the Laplacian for cofinite Kleinian groups with finite-dimensional unitary representations Regularized determinants of the Laplacian for cofinite Kleinian groups with finite-dimensional unitary representations

2006-05-11

arxiv.org/abs/math/0605288v2

Mathematics

Number Theory

To appear in Communications in Mathematical Physics. This is a corrected version

Scientific paper

10.1007/s00220-007-0330-3

For cofinite Kleinian groups (or equivalently, finite-volume
three-dimensional hyperbolic orbifolds) with finite-dimensional unitary
representations, we evaluate the regularized determinant of the Laplacian using
W. Muller's regularization. We give an explicit formula relating the
determinant to the Selberg zeta-function.

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