On the asymptotic distribution of closed geodesics on compact Riemann surfaces

Randol, Burton

doi:10.1090/S0002-9947-1977-0482582-9

On the asymptotic distribution of closed geodesics on compact Riemann surfaces
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Trans. Amer. Math. Soc. 233 (1977), 241-247 Request permission

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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