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Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Dynamical $L$-functions and homology of closed orbits

Author(s): Atsushi Katsuda; Toshikazu Sunada
Journal: Bull. Amer. Math. Soc. 20 (1989), 73-77.
MSC (1985): Primary 58F15, 58F22; Secondary 58F17, 28D20
MathSciNet review: 959209
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References:

1.
T. Adachi, Meromorphic extension of dynamical L-functions, Kumamoto J. Math. 1 (1988), 9-24. MR 951819
2.
T. Adachi and T. Sunada, Homology of closed geodesics in a negatively curved manifold, J. Differential Geom. 26 (1987), 81-99. MR 892032
3.
T. Adachi and T. Sunada, Twisted Perron-Frobenius theorem and L-functions, J. Funct. Anal. 71 (1987), 1-46. MR 879699
4.
R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973), 429-459. MR 339281
5.
M. Denker and W. Philipp, Approximation by Brownian motion for Gibbs measure and flows under a function, Ergodic Theory Dynamical Systems 4 (1984), 541-552. MR 779712
6.
C. Epstein, Asymptotics for closed geodesics in a homology class-finite volume case, Duke Math. J. 55 (1987), 717-757. MR 916117
7.
I. M. Gel'fand and I. I. Pyateckii-Shapiro, A theorem of Poincaré, Dokl. Akad. Nauk 127(1959), 490-493. MR 107738
8.
A. Katsuda and T. Sunada, Homology and closed geodesics in a compact Riemann surface, Amer. J. Math. 109 (1987), 145-156. MR 926741
9.
A. Katsuda, Density theorems for closed orbits, Proc. Taniguchi Sympos. Geometry and Analysis on Manifolds 1987, Lecture Notes in Math., vol. 1339, Springer-Verlag, Berlin and New York, 1988, pp. 182-202. MR 961481
10.
S. Manabe and Y. Ochi, The central limit theorem for current-valued processes induced by geodesic flows, preprint. MR 991288
11.
W. Parry, Bowen 's equidistribution theory and the Dirichlet density theorem, Ergodic Theory Dynamical Systems 4 (1984), 117-134. MR 758898
12.
W. Parry and M. Pollicott, An analogue of the prime number theorem for closed orbits of Axiom A flows, Ann. of Math. (2) 118 (1983), 573-591. MR 727704
13.
W. Parry and M. Pollicott, The Chebotarev theorem for Galois coverings of Axiom A flows, Ergodic Theory Dynamical Systems 6 (1986), 133-148. MR 837980
14.
R. Phillips and P. Sarnak, Geodesics in homology classes, Duke Math. J. 55 (1987), 287-297. MR 894581
15.
J. Plante, Anosov flows, Amer. J. Math. 94 (1972), 729-758. MR 377930
16.
J. Plante, Homology of closed orbits of Anosov flows, Proc. Amer. Math. Soc. 37 (1973), 297-300. MR 310927
17.
M. Pollicott, On the rate of mixing of Axiom A flows, Invent. Math. 81 (1985), 413-426. MR 807065
18.
D. Ruelle, Thermodynamic formalism, Addison-Wesley, Mass., 1978. MR 511655
19.
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. MR 88511
20.
Ya. G. Sinai, Gibbs measure in ergodic tffheory, Russian Math. Surveys 27 (1972), 21-69.
21.
T. Sunada, L-functions in geometry and some applications, Proc. Taniguchi Sympos. 1985, Curvature and Topology of Riemannian Manifolds, Lecture Notes in Math., vol. 1201, Springer-Verlag, Berlin and New York, 1986, pp. 266-284. MR 859591
22.
S. Zelditch, Geodesics in homology classes and periods of automorphic forms, preprint. MR 1113285

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Additional Information:

DOI: 10.1090/S0273-0979-1989-15702-9
PII: S 0273-0979(1989)15702-9


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