The Riemann hypothesis for Selberg’s zeta-function and the asymptotic behavior of eigenvalues of the Laplace operator-Reference-Cited by-同舟云学术

The Riemann hypothesis for Selberg’s zeta-function and the asymptotic behavior of eigenvalues of the Laplace operator

Published:1978 Issue:0 Volume:236 Page:209-223
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Randol Burton

Abstract

Much of that part of the theory of the Riemann zeta-function based on the Riemann hypothesis carries over to zeta-functions of Selberg’s type, and in this way one can get asymptotic information about various eigenvalue problems. The methods are illustrated in the case of a compact Riemann surface.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1978-236-00/S0002-9947-1978-0472728-1/S0002-9947-1978-0472728-1.pdf

Reference12 articles.

1. P. Bérard, Sur la fonction spectrale du Laplacien d’une variété riemannienne compacte sans point conjugués, C. R. Acad. Sci. Paris 283 (1976), 45-48.

2. Die Grundlehren der mathematischen Wissenschaften, Band 167;Chandrasekharan, K.,1970

3. The spectrum of positive elliptic operators and periodic bicharacteristics;Duistermaat, J. J.;Invent. Math.,1975

4. Zeta functions of Selberg’s type for compact space forms of symmetric spaces of rank one;Gangolli, Ramesh;Illinois J. Math.,1977

5. Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II;Huber, Heinz;Math. Ann.,1960

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