Special values of the spectral zeta functions for locally symmetric Riemannian manifolds

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概要

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• In this paper, we establish the formulas expressing the special values of the spectral zeta function ξ<SUB>Δ</SUB>(n) of the Laplacian Δ on some locally symmetric Riemannian manifold Γ\bsla G/K 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 Δ by computing the values ξ<SUB>Δ</SUB>(n) numerically, when Γ\bsla G/K is a Riemann surface with Γ being the quaternion group.

• 社団法人 日本数学会の論文
• 2005-01-01

著者

• Hashimoto Yasufumi

  Graduate School Of Mathematics Kyushu University

関連論文

• Splitting density for lifting about discrete groups
• Special values of the spectral zeta functions for locally symmetric Riemannian manifolds

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