This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
T. Adachi and T. Sunada: Homology of closed geodesics in a negatively curved manifold, preprint.
T. Adachi and T. Sunada: L-functions of dynamical systems and topological graphs, preprint.
T. Adachi: Closed orbits of an Anosov flow and the fundamental group, preprint.
R. Bowen: Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973), 429–460.
R. Brooks: The first eigenvalue in a tower of coverings, preprint.
R. Brooks: Combinatorial problems in spectral geometry, preprint.
D. Fried: Flow equivalence, hyperbolic systems and a new zeta function for flows, Comment. Math. Helvetici 57 (1982), 237–259.
D. Fried: The zeta functions of Ruelle and Selberg I, preprint.
D. Fried: Analytic torsion and closed geodesics on hyperbolic manifolds, preprint.
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.
M. Gromov: Filling Riemannian manifolds, J. Diff. Geom. 18 (1983), 1–147.
D. A. Hejhal: The Selberg trace formula and the Riemann zeta function, Duke Math. J. 43 (1976), 441–482.
D. A. Hejhal: The Selberg Trace Formula for PSL (2, ℝ), I. Springer Lecture Notes 548, 1976.
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.
S. Iyanaga and Y. Kawada (ed.): Encyclopedic Dictionary of Mathematics, MIT Press, Cambridge, 1977.
A. Katsuda: Homology of closed geodesics in a nonpositively curved manifold of rank one, preprint.
N. Kurokawa: On some Euler products. I, Proc. Japan Acad. 60 (1984) 335–338.
N. Kurokawa: On some Euler products. II, Proc. Japan Acad. 60 (1984), 365–368.
S. Lang: Algebraic Number Theory, Addison-Wesley, 1970.
A. Manning: Axiom A diffeomorphisms have rational zeta functions, Bull. London Math. Soc. 3 (1971), 215–220.
H. P. McKean: Selberg's trace formula as applied to a compact Riemann surface, Comm. Pure Appl. Math. 25 (1972), 225–246.
P. Pansu: Croissance des boules et des géodésiques fermées dans les nilvariétés, Ergod. Th. Dynam. Sys. 3 (1983), 415–445.
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.
W. Parry and M. Pollicott: The Chebotarev theorem for Galois coverings of Axiom A flows, preprint.
M. Pollicott: Meromorphic extensions of generalized zeta functions, preprint.
D. Ruelle: Thermodynamic Formalism, Addison-Weasley, Reading, Mass., 1978.
D. Ruelle: Zeta functions for expanding maps and Anosov flows, Invent. Math. 34 (1976), 231–242.
P. Sarnak: Prime geodesic theorems, Ph. D. dissertation, Stanford University (1980).
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.
J. P. Serre: Tree, Springer New York 1980.
S. Smale: Differentiable dynamical systems, Bull. AMS. 73 (1967), 747–817.
T. Sunada: Geodesic flows and geodesic random walks, Advanced Studies in Pure Math. 3 (Geometry of Geodesics and Related Topics) (1984), 47–86.
T. Sunada: Riemannian coverings and isospectral manifolds, Ann. of Math. 121 (1985), 169–186.
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.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this paper
Cite this paper
Sunada, T. (1986). L-functions in geometry and some applications. In: Shiohama, K., Sakai, T., Sunada, T. (eds) Curvature and Topology of Riemannian Manifolds. Lecture Notes in Mathematics, vol 1201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075662
Download citation
DOI: https://doi.org/10.1007/BFb0075662
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16770-9
Online ISBN: 978-3-540-38827-2
eBook Packages: Springer Book Archive