## 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

### Keywords:

functional determinant; Laplacian; sphere