Zeta regularized products and functional determinants on spheres
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 \textit{T. P. Branson} and \textit{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 \(4,6,8\).
scientific article; zbMATH DE number 944415
scientific article