This is a review text file submitted electronically to MR. Reviewer: Thomas Schick Reviewer number: 024016 Address:

FB Mathematik Uni Göttingen Bunsenstr. 3 D-37073 Göttingen Germany schick@uni-math.gwdg.de

Author: Loya, P., McDonald, P., Park, J. Short title: Zeta regularized determinants for conic manifolds Control number: 2274020 Primary classification: 58J52 Secondary classification(s): Review text: The paper studies relative zeta regularized determinants of Laplace type operators on a conic manifold M.

The main results gives a formula for the zeta regularized determinant of the Dirichlet Laplacian relative to the Neumann Laplacian on the conic manifold M, in terms of data given locally near the cone point, as well as global data —(involving the kernels of the Dirichlet and Neumann Laplacians as well as the Dirichlet-to-Neumann operator for the base Γ the cone, considered as boundary of the manifold Y where the cone is cut off M).

This result requires a couple of assumptions, in particular that the Dirichlet Laplacian on Y is invertible, as well as a technical assumption on the Dirichletto-Neumann operator mentioned above.

This result is obtained from a gluing formula for relative determinants of rather general self adjoint extensions of Laplacians.