@article{ASENS_1986_4_19_4_491_0, author = {Fried, David}, title = {The zeta functions of {Ruelle} and {Selberg.} {I}}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {491--517}, publisher = {Elsevier}, volume = {Ser. 4, 19}, number = {4}, year = {1986}, doi = {10.24033/asens.1515}, mrnumber = {88k:58134}, zbl = {0609.58033}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/asens.1515/} }
TY - JOUR AU - Fried, David TI - The zeta functions of Ruelle and Selberg. I JO - Annales scientifiques de l'École Normale Supérieure PY - 1986 SP - 491 EP - 517 VL - 19 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.24033/asens.1515/ DO - 10.24033/asens.1515 LA - en ID - ASENS_1986_4_19_4_491_0 ER -
Fried, David. The zeta functions of Ruelle and Selberg. I. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 19 (1986) no. 4, pp. 491-517. doi : 10.24033/asens.1515. http://archive.numdam.org/articles/10.24033/asens.1515/
[A] Geodesic flows on closed Riemannian manifolds of negative curvature (Proc. Steklov Inst. Math., Vol. 90, 1967). | MR | Zbl
,[AB] Notes on the Lefschetz fixed point theorem for elliptic complexes, Harvard, 1964. | Zbl
and ,[AW] Similarity of automorphisms of the torus (Mem. AMS, Vol. 98, 1970). | MR | Zbl
and ,[BT] Differential forms in algebraic topology, Springer GTM 82, 1982. | MR | Zbl
and ,[B1] Symbolic dynamics for hyperbolic flows (Amer. J. Math., Vol. 95, 1973, pp. 429-460). | MR | Zbl
,[B2] On Axiom A diffeomorphisms (CBMS Reg. Conf. 35, AMS, Providence, 1978). | MR | Zbl
,[Bo] Entire functions, Academic Press, 1954. | MR | Zbl
,[E] Opera omnia, Teubner, 1922.
,[Fr1] Anosov diffeomorphisms (Proc. Symp. Pure Math., Vol. 14, AMS, Providence 1970, pp. 133-164). | MR | Zbl
,[Fr2] Homology and dynamical systems (CBMS Reg. Conf., Vol. 49, AMS, Providence, 1982). | MR | Zbl
,[F1] Homological identities for closed orbits (Inv. Math., Vol. 71, 1984, pp. 419-442). | MR | Zbl
,[F2] Fuchsian groups and Reidemeister torsion (Contemp. Math., Vol. 53, 1986, pp. 141-163). | MR | Zbl
,[F3] Efficiency vs. hyperbolicity on tori, (Springer LNM, Vol. 819, 1980, pp. 175-189). | MR | Zbl
,[F4] Anosov foliations and cohomology (Erg. Th. & Dyn. Syst., Vol. 6, 1986, pp. 9-16). | MR | Zbl
,[F5] Analytic torsion and closed geodesics on hyperbolic manifolds. (Inv. Math., Vol. 84, 1986, pp. 523-540). | MR | Zbl
,[F6] Torsion and closed geodesics on complex hyperbolic manifolds, preprint.
,[G] Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one (Ill. J. Math, Vol. 21, 1977, pp. 1-41). | MR | Zbl
,[G-F] Geodesic flows on manifolds of constant negative curvature (Usp. Mat. Nauk., Vol. 7, 1952, pp. 118-137, and AMS Translations, Vol. 1, 1955, pp. 49-65). | Zbl
and ,[Gr1] La théorie de Fredholm (Bull. Soc. Math. France, Vol. 84, 1956, pp. 319-384). | Numdam | MR | Zbl
,[Gr2] Espaces Nucléaires (Mem. AMS, Vol. 16, Providence, 1955).
,[H] The Selberg trace formula for PSL (2, R), Springer LNM, Vol. 548, 1976 and Vol. 1001, 1983. | MR | Zbl
,[HPS] Invariant manifolds, Springer LNM, Vol. 583, 1977. | MR | Zbl
, and ,[HR] The general theory of Dirichlet series, Cambridge, 1952.
and ,[Ma1] Axiom A diffeomorphisms have rational zeta functions (Bull. London Math. Soc., Vol. 3, 1971, pp. 215-220). | MR | Zbl
,[Ma2] Anosov diffeomorphisms on nilmanifolds (Proc. AMS, Vol. 38, 1973, pp. 423-426). | MR | Zbl
,[M] Closed geodesics and the ƞ-invariant (Annals of Math., Vol. 108, 1978, pp. 1-39). | MR | Zbl
,[PPo] An analogue of the prime number theorem for closed orbits of Axiom A flows (Annals of Math., Vol. 118, 1983, pp. 573-592). | MR | Zbl
and ,[Po] Meromorphic extensions of generalized zeta functions (Inv. Math., Vol. 85, 1986, pp. 147-164). | EuDML | MR | Zbl
,[Ra1] On the asymptotic distribution of closed geodesics on compact Riemann surfaces (Trans. AMS, Vol. 233, 1977, p. 241-247). | MR
,[Ra2] The Selberg trace formula, Chapter XI in Eigenvalues in Riemannian geometry, Academic Press, 1984.
,[R] Markov decomposition for an Y-flow on a three-dimensional manifold (Math. Notes, Vol. 6, pp. 880-886). | MR | Zbl
,[RS] Analytic torsion for complex manifolds (Annals of Math., Vol. 98, 1973, pp. 154-177). | MR | Zbl
and ,[R1] Zeta functions for expanding maps and Anosov flows (Inv. Math., Vol. 34, 1976, pp. 231-242). | EuDML | MR | Zbl
,[R2] Thermodynamic formalism, Addison-Wesley, Reading, 1978. | MR | Zbl
,[Sa] The arithmetic and geometry of some hyperbolic three manifolds (Acta Math., Vol. 151, 1983, pp. 253-295). | MR | Zbl
,[Sc] Selberg type zeta functions for the group of complex two by two matrices of determinant one (Math. Ann., Vol. 253, 1980, pp. 177-194). | EuDML | MR | Zbl
,[S] Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series (J. Indian Math. Soc., Vol. 20, 1956, pp. 47-87). | MR | Zbl
,[Si] Construction of Markov partitions (Func. Anal. Appl., Vol. 2, 1968, pp. 70-80). | Zbl
,[Sm] Differentiable dynamical systems (Bull. AMS, Vol. 73, 1967, pp. 747-817). | MR | Zbl
,[T1] Anosov flows on infra-homogeneous spaces (Proc. Symp. Pure Math, T. 14, Providence, 1970, pp. 299-327). | MR | Zbl
,[T2] On the classification of Anosov flows (Topology, Vol. 14, 1975, pp. 179-189). | MR | Zbl
,[W] Zeta functions of Selberg's type associated with homogeneous vector bundles (Hiroshima Math. J., Vol. 15, 1985, pp. 235-295). | MR | Zbl
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