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An application of the theory of the double gamma function. (English) Zbl 1013.11053
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.
11M06ζ(s) and L(s,χ)
33B15Gamma, beta and polygamma functions
11M35Hurwitz and Lerch zeta functions
33C55Spherical harmonics
58J52Determinants and determinant bundles, analytic torsion