The Riemann hypothesis for Selberg’s zetafunction and the asymptotic behavior of eigenvalues of the Laplace operator
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 by Burton Randol PDF
 Trans. Amer. Math. Soc. 236 (1978), 209223 Request permission
Abstract:
Much of that part of the theory of the Riemann zetafunction based on the Riemann hypothesis carries over to zetafunctions 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.References

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Additional Information
 © Copyright 1978 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 236 (1978), 209223
 MSC: Primary 10H10
 DOI: https://doi.org/10.1090/S00029947197804727281
 MathSciNet review: 0472728