Regularized Determinants of the Laplacian for cofinite kleinian groups with Finite-Dimensional Unitary Representations

摘要

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. Müller’s regularization. We give an explicit formula relating the determinant to the Selberg zeta-function.