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- Publisher
- Springer Journals
- Copyright
- Copyright © 2012 by Springer-Verlag
- Subject
- Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Statistical Physics, Dynamical Systems and Complexity; Classical and Quantum Gravitation, Relativity Theory
- ISSN
- 0010-3616
- eISSN
- 1432-0916
- DOI
- 10.1007/s00220-012-1555-3
- Publisher site
- See Article on Publisher Site
Abstract
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 × 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.
Journal
Communications in Mathematical Physics – Springer Journals
Published: Aug 24, 2012