Honam Mathematical Journal (호남수학학술지)

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

  • Received : 2011.05.18
  • Accepted : 2011.07.18
  • Published : 2011.09.25
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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.

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References

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