Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Homology of closed geodesics in certain Riemannian manifolds


Authors: Atsushi Katsuda and Toshikazu Sunada
Journal: Proc. Amer. Math. Soc. 96 (1986), 657-660
MSC: Primary 58E10; Secondary 53C22
DOI: https://doi.org/10.1090/S0002-9939-1986-0826498-5
MathSciNet review: 826498
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown, by using the trace formula of Selberg type, that every primitive, one-dimensional homology class of a negatively curved compact locally symmetric space contains infinitely many prime closed geodesics.


References [Enhancements On Off] (What's this?)

  • [1] T. Adachi and T. Sunada, $ L$-functions of pro-finite graphs and dynamical systems, preprint, Nagoya, Univ., 1984.
  • [2] Ramesh Gangolli, Zeta functions of Selberg’s type for compact space forms of symmetric spaces of rank one, Illinois J. Math. 21 (1977), no. 1, 1–41. MR 0485702
  • [3] W. Magnus, A. Karras and D. Solitar, Combinatorial group theory, Interscience, New York, 1966.
  • [4] W. Parry and M. Pollicott, The Chebotarev theorem for Galois coverings of axiom $ A$ flows, preprint, Warwick Univ., 1984.
  • [5] A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47–87. MR 0088511
  • [6] T. Sunada, Trace formulas, Wiener integrals and asymptotics, Proc. Spectra Riemannian Manifolds, Kaigai Publ., Tokyo, 1983, pp. 103-113.
  • [7] Toshikazu Sunada, Riemannian coverings and isospectral manifolds, Ann. of Math. (2) 121 (1985), no. 1, 169–186. MR 782558, https://doi.org/10.2307/1971195

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58E10, 53C22

Retrieve articles in all journals with MSC: 58E10, 53C22


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0826498-5
Article copyright: © Copyright 1986 American Mathematical Society