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Zeta regularized products and functional determinants on spheres. (English) Zbl 0864.47024
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 $4,6,8$.

MSC:
47F05Partial differential operators
58J50Spectral problems; spectral geometry; scattering theory
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Full Text: DOI Link
References:
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