DETERMINANTS OF THE LAPLACIANS ON THE n-DIMENSIONAL UNIT SPHERE S n (n

During the last three decades, the problem of evaluation of the determinants of the Laplacians on Riemann manifolds has received considerable attention by many authors. The functional determinant for the n-dimensional sphere with the standard metric has been computed in several ways. Here we aim at computing the determinants of the Laplacians on (n = 8, 9) by mainly using ceratin known closed-form evaluations of series involving Zeta function.