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http://dx.doi.org/10.5831/HMJ.2011.33.3.321

DETERMINANTS OF THE LAPLACIANS ON THE n-DIMENSIONAL UNIT SPHERE Sn (n = 8, 9)  

Choi, June-Sang (Department of Mathematics, Dongguk University)
Publication Information
Honam Mathematical Journal / v.33, no.3, 2011 , pp. 321-333 More about this Journal
Abstract
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 $S^n$ with the standard metric has been computed in several ways. Here we aim at computing the determinants of the Laplacians on $S^n$ (n = 8, 9) by mainly using ceratin known closed-form evaluations of series involving Zeta function.
Keywords
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;
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