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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DOI:
http://dx.doi.org/10.1090/S0002-9947-1977-0482582-9

Article copyright:
© Copyright 1977
American Mathematical Society