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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the asymptotic distribution of closed geodesics on compact Riemann surfaces
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by Burton Randol PDF
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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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 233 (1977), 241-247
  • MSC: Primary 53C20; Secondary 10D15, 30A58, 58G99
  • DOI: https://doi.org/10.1090/S0002-9947-1977-0482582-9
  • MathSciNet review: 0482582