The Spectral Zeta Function for Laplace Operators on Warped Product Manifolds of the type $I\times_{f} N$

Details The Spectral Zeta Function for Laplace Operators on Warped Product Manifolds of the type $I\times_{f} N$ The Spectral Zeta Function for Laplace Operators on Warped Product Manifolds of the type $I\times_{f} N$

2011-11-08

arxiv.org/abs/1111.2010v1

Physics

Mathematical Physics

29 pages, LaTeX

Scientific paper

In this work we study the spectral zeta function associated with the Laplace operator acting on scalar functions defined on a warped product of manifolds of the type $I\times_{f} N$ where $I$ is an interval of the real line and $N$ is a compact, $d$-dimensional Riemannian manifold either with or without boundary. Starting from an integral representation of the spectral zeta function, we find its analytic continuation by exploiting the WKB asymptotic expansion of the eigenfunctions of the Laplace operator on $M$ for which a detailed analysis is presented. We apply the obtained results to the explicit computation of the zeta regularized functional determinant and the coefficients of the heat kernel asymptotic expansion.

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