The BFK-gluing Formula for Zeta-determinants and the Conformal Rescaling of a Metric

초록

The Dirichlet-to-Neumann operator plays a central role in the BFK-gluing formula for zeta-determinants of Laplacians, whose homogeneous symbols are invariants with respect to conformal rescaling of Riemannian metrics. We use this property together with the result in Kirsten and Lee (J Math Phys 58(12):123501, 19p, 2015) to recover the main result of Kirsten and Lee (J Spectr Theory 10:1007–1051, 2020), which reduces much of long and tedious computation. We also use this property to prove some relation about the value at zero of the zeta function associated to the Dirichlet-to-Neumann operator, which is obtained in Kirsten and Lee (J Geom Anal 28:3856–3891, 2018) on a warped product manifold. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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