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

• Journal title : Honam Mathematical Journal
• Volume 33, Issue 3,  2011, pp.321-333
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2011.33.3.321
Title & Authors
DETERMINANTS OF THE LAPLACIANS ON THE n-DIMENSIONAL UNIT SPHERE Sn (n = 8, 9)
Choi, June-Sang;

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 $\small{S^n}$ with the standard metric has been computed in several ways. Here we aim at computing the determinants of the Laplacians on $\small{S^n}$ (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;
Language
English
Cited by
1.
Determinants of the Laplacians on the n-dimensional unit sphere Sn, Advances in Difference Equations, 2013, 2013, 1, 236
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