DETERMINANTS OF THE LAPLACIANS ON THE n-DIMENSIONAL UNIT SPHERE S<sup>n</sup>(n = 8, 9)

Junesang Choi

Type: Article

Publication Date: 2011-09-25

Citations: 3

DOI: https://doi.org/10.5831/hmj.2011.33.3.321

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 <TEX>$S^n$</TEX> with the standard metric has been computed in several ways. Here we aim at computing the determinants of the Laplacians on <TEX>$S^n$</TEX> (n = 8, 9) by mainly using ceratin known closed-form evaluations of series involving Zeta function.

Locations

Honam Mathematical Journal - View - PDF

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Works Cited by This (17)

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+	Series Associated with the Zeta and Related Functions	2001	H. M. Srivastava Junesang Choi
+	Harmonic Analysis on Symmetric Spaces and Applications I	1985	Audrey Terras
+ PDF Chat	Some series involving the zeta function	1995	Junesang Choi H. M. Srivastava J. R. Quine
+ PDF Chat	On determinants of Laplacians on Riemann surfaces	1986	Eric D’Hoker D. H. Phong
+ PDF Chat	Zeta regularized products	1993	J. R. Quine Somayeh Heydari R. Song
+ PDF Chat	Determinants of Laplacians	1987	Peter Sarnak
+ PDF Chat	AN APPLICATION OF THE THEORY OF THE DOUBLE GAMMA FUNCTION	1999	Junesang Choi H. M. Srivástava
+	Series involving the Zeta function and multiple Gamma functions	2003	Junesang Choi Young Joon Cho H. M. Srivastava
+ PDF Chat	Spectral functions, special functions and the Selberg zeta function	1987	A. Voros
+ PDF Chat	Zeta Regularized Products and Functional Determinants on Spheres	1996	J. R. Quine Junesang Choi