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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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참고문헌 (19)
참고문헌 신청
C. Kassel / 1989 / Le residu non commutatif (d’apres M. Wodzicki), Seminaire Bourbaki, Vol. 1988/89
D. Burghelea / 1992 / Meyer-Vietoris type formula for determinants of elliptic differential operators / Journal of Functional Analysis 107 (1) : 34 ~ 65
G. Carron / 2002 / Determinant relatif et la fonction Xi / American Journal of Mathematics 124 (2) : 307 ~ 352
G. Grubb / 1995 / Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems / Inventiones mathematicae 121 (3) : 481 ~ 529
J. Muller / 2006 / Regularized determinants of Laplace-type operators, analytic surgery, and relative determinants / Duke Mathematical Journal 133 (2) : 259 ~ 312
D. Burghelea / 1992 / Meyer-Vietoris type formula for determinants of elliptic differential operators / Journal of Functional Analysis 107 (1) : 34 ~ 65
G. Carron / 2002 / Determinant relatif et la fonction Xi / American Journal of Mathematics 124 (2) : 307 ~ 352
G. Grubb / 1995 / Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems / Inventiones mathematicae 121 (3) : 481 ~ 529
J. Muller / 2006 / Regularized determinants of Laplace-type operators, analytic surgery, and relative determinants / Duke Mathematical Journal 133 (2) : 259 ~ 312
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Erratum ``The BFK-gluing formula for zeta-determinants and the value of relative zeta functions at zero" [J. Korean Math. Soc. 45 (2008), No. 5, pp. 1255--1274]
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