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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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A local limit theorem for closed geodesics and homology
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by Richard Sharp PDF
Trans. Amer. Math. Soc. 356 (2004), 4897-4908 Request permission

Abstract:

In this paper, we study the distribution of closed geodesics on a compact negatively curved manifold. We concentrate on geodesics lying in a prescribed homology class and, under certain conditions, obtain a local limit theorem to describe the asymptotic behaviour of the associated counting function as the homology class varies.
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Additional Information
  • Richard Sharp
  • Affiliation: Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
  • MR Author ID: 317352
  • Email: sharp@maths.man.ac.uk
  • Received by editor(s): March 28, 2003
  • Received by editor(s) in revised form: June 6, 2003
  • Published electronically: January 16, 2004
  • Additional Notes: The author was supported by an EPSRC Advanced Research Fellowship
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 4897-4908
  • MSC (2000): Primary 37C27, 37C30, 37D20, 37D40, 53C22
  • DOI: https://doi.org/10.1090/S0002-9947-04-03534-2
  • MathSciNet review: 2084404