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Zbl 0864.47024
Quine, J.R.; Choi, J.
Zeta regularized products and functional determinants on spheres.
(English)
[J] Rocky Mt. J. Math. 26, No.2, 719-729 (1996). ISSN 0035-7596

The authors use a factorization theorem for zeta regularized products to compute the functional determinant of the Laplacian on the sphere $S^n$ with the standard metric. They also determine the functional determinant of the conformal Laplacian on an even-dimensional sphere. The computations in this paper agree with those of {\it T. P. Branson} and {\it B. Ørsted} [Proc. Am. Math. Soc. 113, No. 3, 669-682 (1991; Zbl 0762.47019)]. The authors list the values of the functional determinant for the ordinary Laplacian in dimensions $n=2,3,4,5,6$ and for the conformal Laplacian in dimensions $4,6,8$.
[P.Gilkey (Eugene)]
MSC 2000:
*47F05 Partial differential operators
58J50 Spectral problems; spectral geometry; scattering theory

Keywords: factorization theorem; zeta regularized products; functional determinant of the Laplacian

Citations: Zbl 0762.47019

Cited in: Zbl 0946.11021

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