Determinant of Laplacian on a non-compact 3-dimensional hyperbolic   manifold with finite volume
  The functional determinant of Laplace-type operators on the 3-dimensional non-compact hyperbolic manifold with invariant fundamental domain of finite volume is computed by quadratures and making use of the related terms of the Selberg trace formula. 
A.A. Bytsenko, Guido Cognola and Sergio Zerbini