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Determinant of Laplacian on \(S^ 3\). (English) Zbl 0806.58053

The author computes the functional determinant of the Laplacian on the sphere \(S^ n\) with the standard metric for \(n = 1,2,3\) by factorizing the shifted functional determinant into multiple gamma functions; this is then used to evaluate the unshifted determinant. This result agrees with a previous result by Vardi for \(n = 1,2\) and disagrees if \(n = 3\).
Reviewer: P.Gilkey (Eugene)

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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