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

 

On the asymptotic distribution of closed geodesics on compact Riemann surfaces


Author: Burton Randol
Journal: Trans. Amer. Math. Soc. 233 (1977), 241-247
MSC: Primary 53C20; Secondary 10D15, 30A58, 58G99
MathSciNet review: 0482582
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Abstract: The set of lengths of closed geodesics on a compact Riemann surface is related to the Selberg zeta function in a manner which is evocative of the relationship between the rational primes and the Riemann zeta function. In this paper, this connection is developed to derive results about the asymptotic distribution of these lengths.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0482582-9
PII: S 0002-9947(1977)0482582-9
Article copyright: © Copyright 1977 American Mathematical Society