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January, 2005 Special values of the spectral zeta functions for locally symmetric Riemannian manifolds
Yasufumi HASHIMOTO
J. Math. Soc. Japan 57(1): 217-232 (January, 2005). DOI: 10.2969/jmsj/1160745823

Abstract

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

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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

Information

Published: January, 2005
First available in Project Euclid: 13 October 2006

zbMATH: 1084.11052
MathSciNet: MR2114730
Digital Object Identifier: 10.2969/jmsj/1160745823

Subjects:
Primary: 11F72
Secondary: 11M36 , 35P15

Keywords: first eigenvalue , Selberg's zeta function , spectral zeta function

Rights: Copyright © 2005 Mathematical Society of Japan

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Vol.57 • No. 1 • January, 2005
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