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 T. P. Branson and 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 \(4,6,8\).
Reviewer: P.Gilkey (Eugene)


47F05 General theory of partial differential operators
58J50 Spectral problems; spectral geometry; scattering theory on manifolds


Zbl 0762.47019
Full Text: DOI Link


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