Abstract
In this paper, we establish the formulas expressing the special values of the spectral zeta function of the Laplacian on some locally symmetric Riemannian manifold in terms of the coefficients of the Laurent expansion of the corresponding Selberg zeta function. As an application, we give a numerical estimation of the first eigenvalue of by computing the values numerically, when is a Riemann surface with being the quaternion group.
Citation
Yasufumi HASHIMOTO. "Special values of the spectral zeta functions for locally symmetric Riemannian manifolds." J. Math. Soc. Japan 57 (1) 217 - 232, January, 2005. https://doi.org/10.2969/jmsj/1160745823
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