Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE BFK-GLUING FORMULA FOR ZETA-DETERMINANTS AND THE VALUE OF RELATIVE ZETA FUNCTIONS AT ZERO

  • Published : 2008.09.30
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Abstract

The purpose of this paper is to discuss the constant term appearing in the BFK-gluing formula for the zeta-determinants of Laplacians on a complete Riemannian manifold when the warped product metric is given on a collar neighborhood of a cutting compact hypersurface. If the dimension of a hypersurface is odd, generally this constant is known to be zero. In this paper we describe this constant by using the heat kernel asymptotics and compute it explicitly when the dimension of a hypersurface is 2 and 4. As a byproduct we obtain some results for the value of relative zeta functions at s=0.

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References

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  1. Relative zeta-determinants of Dirac Laplacians on a half-infinite cylinder with boundary conditions in the smooth, self-adjoint Grassmannian vol.59, pp.8, 2009, https://doi.org/10.1016/j.geomphys.2009.05.002
  2. The Burghelea-Friedlander-Kappeler–gluing formula for zeta-determinants on a warped product manifold and a product manifold vol.56, pp.12, 2015, https://doi.org/10.1063/1.4936074