摘要：During the last three decades, the problem of evaluation of the determinants of the Laplacians on Riemann manifolds has received considerable attention from many authors. The functional determinant for the k-dimensional unit sphere S k with the standard metric has been computed in several ways. Here we aim at computing the determinants of the Laplacians on S k ( k = 2 n + 1 ) by mainly using certain closed-form evaluations of the series involving zeta function. MSC:11M35, 11M36, 11M06, 33B15.
关键词：gamma function ; psi- (or digamma) function ; Riemann zeta function ; Hurwitz zeta function ; Selberg zeta function ; zeta regularized product ; determinants of Laplacians ; series associated with the zeta functions
