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Zbl 1013.11053
Choi, Junesang; Srivastava, H.M.
An application of the theory of the double gamma function. (English)
[J] Kyushu J. Math. 53, No.1, 209-222 (1999). ISSN 1340-6116

Authors' summary: The main purpose of this paper is first to show how one can apply the theory of the double Gamma function, which has recently been revived in the study of the determinants of Laplacians, to evaluate some classes of series involving the zeta-function. The determinants of Laplacians on the $n$-sphere $S^n$ ($n=1,2,3)$ are computed by using our evaluations of series involving the zeta-function. Relevant connections of the results presented here with those given in earlier works are also pointed out.
[Hari M.Srivastava (Victoria)]

MSC 2000:: *11M06 Riemannian zeta-function and Dirichlet L-function
33B15 Gamma-functions, etc.
11M35 Other zeta functions
33C55 Elliptic integrals as hypergeometric functions
58J52 Determinants and determinant bundles, analytic torsion

Keywords: double Gamma function; determinants of Laplacians; evaluations of series; zeta-function

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