L-functions in geometry and some applications

  • Toshikazu Sunada
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1201)

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References

  1. 1.
    T. Adachi and T. Sunada: Homology of closed geodesics in a negatively curved manifold, preprint.Google Scholar
  2. 2.
    T. Adachi and T. Sunada: L-functions of dynamical systems and topological graphs, preprint.Google Scholar
  3. 3.
    T. Adachi: Closed orbits of an Anosov flow and the fundamental group, preprint.Google Scholar
  4. 4.
    R. Bowen: Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973), 429–460.MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    R. Brooks: The first eigenvalue in a tower of coverings, preprint.Google Scholar
  6. 6.
    R. Brooks: Combinatorial problems in spectral geometry, preprint.Google Scholar
  7. 7.
    D. Fried: Flow equivalence, hyperbolic systems and a new zeta function for flows, Comment. Math. Helvetici 57 (1982), 237–259.MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    D. Fried: The zeta functions of Ruelle and Selberg I, preprint.Google Scholar
  9. 9.
    D. Fried: Analytic torsion and closed geodesics on hyperbolic manifolds, preprint.Google Scholar
  10. 10.
    R. Gangolli: Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one, III. J. Math. 21 (1977), 1–42.MathSciNetMATHGoogle Scholar
  11. 11.
    M. Gromov: Filling Riemannian manifolds, J. Diff. Geom. 18 (1983), 1–147.MathSciNetMATHGoogle Scholar
  12. 12.
    D. A. Hejhal: The Selberg trace formula and the Riemann zeta function, Duke Math. J. 43 (1976), 441–482.MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    D. A. Hejhal: The Selberg Trace Formula for PSL (2, ℝ), I. Springer Lecture Notes 548, 1976.Google Scholar
  14. 14.
    Y. Ihara: On discrete subgroups of the two by two projective linear group over p-adic fields, J. Math. Soc. Japan 18 (1966), 219–235.MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    S. Iyanaga and Y. Kawada (ed.): Encyclopedic Dictionary of Mathematics, MIT Press, Cambridge, 1977.Google Scholar
  16. 16.
    A. Katsuda: Homology of closed geodesics in a nonpositively curved manifold of rank one, preprint.Google Scholar
  17. 17.
    N. Kurokawa: On some Euler products. I, Proc. Japan Acad. 60 (1984) 335–338.MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    N. Kurokawa: On some Euler products. II, Proc. Japan Acad. 60 (1984), 365–368.MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    S. Lang: Algebraic Number Theory, Addison-Wesley, 1970.Google Scholar
  20. 20.
    A. Manning: Axiom A diffeomorphisms have rational zeta functions, Bull. London Math. Soc. 3 (1971), 215–220.MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    H. P. McKean: Selberg's trace formula as applied to a compact Riemann surface, Comm. Pure Appl. Math. 25 (1972), 225–246.MathSciNetCrossRefGoogle Scholar
  22. 22.
    P. Pansu: Croissance des boules et des géodésiques fermées dans les nilvariétés, Ergod. Th. Dynam. Sys. 3 (1983), 415–445.MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    W. Parry and M. Pollicott: An analogue of the prime number theorem for closed orbits of Axiom A flows, Ann. of Math. 118 (1983), 573–591.MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    W. Parry and M. Pollicott: The Chebotarev theorem for Galois coverings of Axiom A flows, preprint.Google Scholar
  25. 25.
    M. Pollicott: Meromorphic extensions of generalized zeta functions, preprint.Google Scholar
  26. 26.
    D. Ruelle: Thermodynamic Formalism, Addison-Weasley, Reading, Mass., 1978.MATHGoogle Scholar
  27. 27.
    D. Ruelle: Zeta functions for expanding maps and Anosov flows, Invent. Math. 34 (1976), 231–242.MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    P. Sarnak: Prime geodesic theorems, Ph. D. dissertation, Stanford University (1980).Google Scholar
  29. 29.
    A. Selberg: Harmonic analysis and discontinuous subgroups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. 20 (1956), 47–87.MathSciNetMATHGoogle Scholar
  30. 30.
    J. P. Serre: Tree, Springer New York 1980.CrossRefGoogle Scholar
  31. 31.
    S. Smale: Differentiable dynamical systems, Bull. AMS. 73 (1967), 747–817.MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    T. Sunada: Geodesic flows and geodesic random walks, Advanced Studies in Pure Math. 3 (Geometry of Geodesics and Related Topics) (1984), 47–86.Google Scholar
  33. 33.
    T. Sunada: Riemannian coverings and isospectral manifolds, Ann. of Math. 121 (1985), 169–186.MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    T. Sunada: Number theoretic methods in spectral geometry, to appear in Proc. The 6th Symp. on Differential Geometry and Differential Equations held at Shanghai, China 1985.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Toshikazu Sunada
    • 1
  1. 1.Department of MathematicsNagoya UniversityNagoyaJapan

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