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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: Burton Randol
Journal: Trans. Amer. Math. Soc. 236 (1978), 209-223
MSC: Primary 10H10
MathSciNet review: 0472728
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0472728-1
PII: S 0002-9947(1978)0472728-1
Article copyright: © Copyright 1978 American Mathematical Society