Distribution of closed geodesics on the modular surface and quadratic irrationals

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1. [1] ADLER (R.) and FLATTO (L.). — Cross section maps for geodesic flows, I, in Ergodic Theory and Dynamical Systems II, KATOK (A.) Ed., Birkhäuser, Stuttgart, 1982. Zbl0496.58009MR84h:58113
2. [2] ARNOLD (V. I.) and AVEZ (A.). — Ergodic problems of classical mechanics, Benjamin, New York, 1968. Zbl0167.22901MR38 #1233
3. [3] BILLINGSLEY (P.). — Ergodic theory and information, Wiley, New York, 1965. Zbl0141.16702MR33 #254
4. [4] BOWEN (R.). — The equidistribution of closed geodesics, Amer. J. Math., Vol. 94, 1972, pp. 413-423. Zbl0249.53033MR47 #4291
5. [5] DAVENPORT (H.). — Multiplicative number theory, G.T.M., 74, Springer, New York, 1980. Zbl0453.10002MR82m:10001
6. [6] DAVENPORT (H.) and SCHMIDT (W. M.). — Approximation to real numbers by quadratic irrationals, Acta Arith., Vol. 14, 1967, p. 209-223. MR37 #1321
7. [7] DICKSON (L. E.). — History of the theory of numbers II, Chelsea, New York, 1971. 
8. [8] GUNNING (R. C.). — Lectures on modular forms, P.U.P., Princeton, 1962. Zbl0178.42901MR24 #A2664
9. [9] HARDY (G. H.) and WRIGHT (E. M.). — An introduction to the theory of numbers, O.U.P., Oxford, 1983. Zbl0020.29201JFM64.0093.03
10. [10] MAYER (D. H.). — On a zeta function related to the continued fraction transformation, Bull. Soc. Math. Fr., T. 104, 1976, pp. 195-203. Zbl0328.58011MR54 #6210
11. [11] PARRY (W.). — Bowen's equidistribution theory and the Dirichlet density theorem, Ergod. Th. & Dynam. Sys., Vol. 4, 1984, pp. 117-134. Zbl0567.58014MR86j:58125
12. [12] PARRY (W.) and POLLICOTT (M.). — An analogue of the prime number theorem for closed orbits of Axiom A flows, Annals of Math., Vol. 118, 1983, pp. 573-591. Zbl0537.58038MR85i:58105
13. [13] PARTHASARATHY (K. R.). — Introduction to probability and measure, MacMillan, India, 1980. Zbl0395.28001
14. [14] POLLICOTT (M.). — A complex Ruelle-Perron-Frobenius theorem and two counter-examples, Ergod. Th. and Dynam. Sys., Vol. 4, 1984, pp. 135-146. Zbl0575.47009MR88i:58097
15. [15] RUELLE (D.). — Zeta functions for expanding maps and Anosov flows, Invent. Math., Vol. 34, 1976, pp. 231-242. Zbl0329.58014MR54 #8732
16. [16] RUELLE (D.). — Thermodynamic Formalism, Addison-Wesley, Mass., 1978. Zbl0401.28016MR80g:82017
17. [17] SARNAK (P.). — Class numbers of indefinite binary quadratic forms, J. Number Theory, Vol. 15, 1982, pp. 229-247. Zbl0499.10021MR84i:10023a
18. [18] SERIES (C.). — The modular surface and continued fractions, J. London Math. Soc. (to appear). Zbl0545.30001
19. [19] SERIES (C.). — On coding geodesics with continued fractions, Enseignement Mathématique, Vol. 29, Univ. de Genève, 1980, pp. 67-76. Zbl0476.58018MR82h:30052
20. [20] SERRE (J.-P.). — A course in arithmetic, G.T.M., 7, Springer, Berlin, 1973. Zbl0256.12001MR49 #8956
21. [21] TITCHMARSH (E. C.). — The theory of functions, O.U.P., Oxford, 1983. Zbl0005.21004
22. [22] WALTERS (P.). — Invariant measures and equilibrium states for some mappings which expand distances, Trans. Amer. Math. Soc., Vol. 236, 1978, pp. 212-153. Zbl0375.28009MR57 #6371
23. [23] WIENER (N.). — The Fourier integral and certain of its applications, C.U.P., Cambridge, 1933. Zbl0006.05401JFM59.0416.01

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