THE BFK-GLUING FORMULA FOR ZETA-DETERMINANTS AND THE VALUE OF RELATIVE ZETA FUNCTIONS AT ZERO

- Journal title : Journal of the Korean Mathematical Society
- Volume 45, Issue 5, 2008, pp.1255-1274
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2008.45.5.1255

Title & Authors

THE BFK-GLUING FORMULA FOR ZETA-DETERMINANTS AND THE VALUE OF RELATIVE ZETA FUNCTIONS AT ZERO

Lee, Yoon-Weon;

Lee, Yoon-Weon;

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.

Keywords

(relative) zeta-determinant;BFK-gluing formula;Dirichlet-to-Neumann operator;Dirichlet boundary condition;warped product metric;

Language

English

Cited by

1.

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