The Polynomial Associated with the BFK-Gluing Formula of the Zeta-Determinant on a Compact Warped Product Manifold
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In the proof of the BFK-gluing formula of the zeta-determinant of a Laplacian there appears a polynomial of degree less than half of the dimension of an underlying manifold. This polynomial is determined completely by some data on a collar neighborhood of a cutting compact hypersurface. In this paper we compute the polynomial in terms of a warping function when a collar neighborhood of a cutting hypersurface is a warped product manifold. We also use a similar method to compute the values of a relative zeta function and a zeta function associated to the Dirichlet-to-Neumann operator at zero on a warped product manifold.
KeywordsBFK-gluing formula Relative zeta-determinant Dirichlet-to-Neumann operator Warped product metric Warping function
Mathematics Subject ClassificationPrimary: 58J20 Secondary: 14F40
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