The zeta functions of Ruelle and Selberg. I
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 19 (1986) no. 4, pp. 491-517. 
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     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 = {https://www.numdam.org/articles/10.24033/asens.1515/}
}
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Fried, David. The zeta functions of Ruelle and Selberg. I. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 19 (1986) no. 4, pp. 491-517. doi : 10.24033/asens.1515. https://www.numdam.org/articles/10.24033/asens.1515/

[A] D. Anosov, Geodesic flows on closed Riemannian manifolds of negative curvature (Proc. Steklov Inst. Math., Vol. 90, 1967). | MR | Zbl

[AB] M. Atiyah and R. Bott, Notes on the Lefschetz fixed point theorem for elliptic complexes, Harvard, 1964. | Zbl

[AW] R. Adler and B. Weiss, Similarity of automorphisms of the torus (Mem. AMS, Vol. 98, 1970). | MR | Zbl

[BT] R. Bott and L. Tu, Differential forms in algebraic topology, Springer GTM 82, 1982. | MR | Zbl

[B1] R. Bowen, Symbolic dynamics for hyperbolic flows (Amer. J. Math., Vol. 95, 1973, pp. 429-460). | MR | Zbl

[B2] R. Bowen, On Axiom A diffeomorphisms (CBMS Reg. Conf. 35, AMS, Providence, 1978). | MR | Zbl

[Bo] R. Boas, Entire functions, Academic Press, 1954. | MR | Zbl

[E] L. Euler, Opera omnia, Teubner, 1922.

[Fr1] J. Franks, Anosov diffeomorphisms (Proc. Symp. Pure Math., Vol. 14, AMS, Providence 1970, pp. 133-164). | MR | Zbl

[Fr2] J. Franks, Homology and dynamical systems (CBMS Reg. Conf., Vol. 49, AMS, Providence, 1982). | MR | Zbl

[F1] D. Fried, Homological identities for closed orbits (Inv. Math., Vol. 71, 1984, pp. 419-442). | MR | Zbl

[F2] D. Fried, Fuchsian groups and Reidemeister torsion (Contemp. Math., Vol. 53, 1986, pp. 141-163). | MR | Zbl

[F3] D. Fried, Efficiency vs. hyperbolicity on tori, (Springer LNM, Vol. 819, 1980, pp. 175-189). | MR | Zbl

[F4] D. Fried, Anosov foliations and cohomology (Erg. Th. & Dyn. Syst., Vol. 6, 1986, pp. 9-16). | MR | Zbl

[F5] D. Fried, Analytic torsion and closed geodesics on hyperbolic manifolds. (Inv. Math., Vol. 84, 1986, pp. 523-540). | MR | Zbl

[F6] D. Fried, Torsion and closed geodesics on complex hyperbolic manifolds, preprint.

[G] R. Gangolli, 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] I. Gelfand and S. Fomin, 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

[Gr1] A. Grothendieck, La théorie de Fredholm (Bull. Soc. Math. France, Vol. 84, 1956, pp. 319-384). | Numdam | MR | Zbl

[Gr2] A. Grothendieck, Espaces Nucléaires (Mem. AMS, Vol. 16, Providence, 1955).

[H] D. Hejhal, The Selberg trace formula for PSL (2, R), Springer LNM, Vol. 548, 1976 and Vol. 1001, 1983. | MR | Zbl

[HPS] M. Hirsch, C. Pugh and M. Shub, Invariant manifolds, Springer LNM, Vol. 583, 1977. | MR | Zbl

[HR] G. Hardy and M. Riesz, The general theory of Dirichlet series, Cambridge, 1952.

[Ma1] A. Manning, Axiom A diffeomorphisms have rational zeta functions (Bull. London Math. Soc., Vol. 3, 1971, pp. 215-220). | MR | Zbl

[Ma2] A. Manning, Anosov diffeomorphisms on nilmanifolds (Proc. AMS, Vol. 38, 1973, pp. 423-426). | MR | Zbl

[M] J. Millson, Closed geodesics and the ƞ-invariant (Annals of Math., Vol. 108, 1978, pp. 1-39). | MR | Zbl

[PPo] W. Perry and M. Pollicott, 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

[Po] M. Pollicott, Meromorphic extensions of generalized zeta functions (Inv. Math., Vol. 85, 1986, pp. 147-164). | EuDML | MR | Zbl

[Ra1] B. Randol, On the asymptotic distribution of closed geodesics on compact Riemann surfaces (Trans. AMS, Vol. 233, 1977, p. 241-247). | MR

[Ra2] B. Randol, The Selberg trace formula, Chapter XI in Eigenvalues in Riemannian geometry, Academic Press, 1984.

[R] M. Ratner, Markov decomposition for an Y-flow on a three-dimensional manifold (Math. Notes, Vol. 6, pp. 880-886). | MR | Zbl

[RS] D. Ray and I. Singer, Analytic torsion for complex manifolds (Annals of Math., Vol. 98, 1973, pp. 154-177). | MR | Zbl

[R1] D. Ruelle, Zeta functions for expanding maps and Anosov flows (Inv. Math., Vol. 34, 1976, pp. 231-242). | EuDML | MR | Zbl

[R2] D. Ruelle, Thermodynamic formalism, Addison-Wesley, Reading, 1978. | MR | Zbl

[Sa] P. Sarnak, The arithmetic and geometry of some hyperbolic three manifolds (Acta Math., Vol. 151, 1983, pp. 253-295). | MR | Zbl

[Sc] D. Scott, 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] A. Selberg, 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] Y. Sinai, Construction of Markov partitions (Func. Anal. Appl., Vol. 2, 1968, pp. 70-80). | Zbl

[Sm] S. Smale, Differentiable dynamical systems (Bull. AMS, Vol. 73, 1967, pp. 747-817). | MR | Zbl

[T1] P. Tomter, Anosov flows on infra-homogeneous spaces (Proc. Symp. Pure Math, T. 14, Providence, 1970, pp. 299-327). | MR | Zbl

[T2] P. Tomter, On the classification of Anosov flows (Topology, Vol. 14, 1975, pp. 179-189). | MR | Zbl

[W] M. Wakayama, 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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