Advanced Studies in Pure Mathematics

Spectral Zeta Functions

André Voros

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This article gives a survey of various generalizations of Riemann’s $\zeta$-function, associated with operator spectra and which may be generically called spectral zeta functions. Areas of application include Riemannian geometry (the spectrum of the Laplacian) and quantum mechanics. We review one example of each class in concrete detail: the Laplacian on a compact surface of constant negative curvature, and the Schrödinger operator on the real line with a homogeneous potential $q^{2M}$ ($M$ a positive integer).

Article information

Zeta Functions in Geometry, N. Kurokawa and T. Sunada, eds. (Tokyo: Mathematical Society of Japan, 1992), 327-358

Received: 20 January 1991
First available in Project Euclid: 15 August 2018

Permanent link to this document euclid.aspm/1534359133

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Voros, André. Spectral Zeta Functions. Zeta Functions in Geometry, 327--358, Mathematical Society of Japan, Tokyo, Japan, 1992. doi:10.2969/aspm/02110327.

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