Distribution of eigenvalues for the modular group

Communications in Mathematical Physics

Volumn 176, Issue 3, 1996, Pages 577-617

  Bogomolny, E ^a,b   Leyvraz, F ^a,c   Schmit, C ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

^c UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030541938     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02099251     Document Type: Article

References (45)

1. Hopf, E.: Ergodentheorie. Berlin, Heidelberg, New York: Springer 1937
2. Encyclopedia of Mathematical Sciences, Vol. 1 Dynamical Systems, eds. D.V. Arnold, V.I. Anosov, Berlin, Heidelberg, New York: Springer 1988
3. Balazs, N.L., Voros, A.: Phys. Rep. 143, 109 (1986)
4. Proceedings of the Les Houches Summer School (1989) Chaos and Quantum Physics. Giannoni, M.J., Voros, A., Zinn-Justin, J. (eds.) Amsterdam: North Holland, 1991
5. Gutzwiller, M.C.: Chaos in Classical and Quantum Mechanics. Berlin, Heidelberg, New York: Springer 1990
6. Selberg, A.: J. Ind. Math. Soc. 20, 47 (1956)
7. Hejhal, D.: The Selberg Trace Formula for PSL (2, R). Vol. 1 Lecture Notes in Mathematics 548 (1979); Vol. 2, ibid. 1001 (1983)
8. Hejhal, D.: The Selberg Trace Formula for PSL (2, R). Vol. 1 Lecture Notes in Mathematics 548 (1979); Vol. 2, ibid. 1001 (1983)
9. Gutzwiller, M.C.: J. Math. Phys. 12, 343 (1971)
10. Bohigas, O., Giannoni, M.-J., Schmit, C.: Phys. Rev. Lett. 52, 1 (1984); J. Physique Lettres 45, L1015 (1984)
11. Bohigas, O., Giannoni, M.-J., Schmit, C.: Phys. Rev. Lett. 52, 1 (1984); J. Physique Lettres 45, L1015 (1984)
12. Mehta, M.L.: Random Matrices and the Statistical Theory of Energy Levels. New York Academic Press, 1967
13. Schmit, C.: In: [4]
14. Schmit, C.: Triangular Billiards on the Hyperbolic Plane: Spectral Properties. Report IPNO/TH (1991) (unpublished)
15. Aurich, R., Steiner, F.: Physica D 39, 169 (1989)
16. Aurich, R., Steiner, F.: Physica D 43, 155 (1990)
17. Berry, M.V., Tabor, M.: Proc. R. Soc. London A 356, 375 (1977)
18. Bogomolny, E., Georgeot, B., Giannoni, M.-J., Schmit, C.: Phys. Rev. Lett. 69, 1477 (1992)
19. Bolte, J., Steil, G., Steiner, F.: Phys. Rev. Lett. 69, 2188 (1992)
20. Bogomolny, E., Georgeot, B., Giannoni, M.-J., Schmit, C.: Arithmetical Chaos. Preprint IPNO/TH 93-51
21. Bolte, J.: Ph.D. Thesis DESY (1993)
22. Gelfand, I.M., Graev, M.I., Pyatetskii-Shapiro, I.I.: Representation Theory and Automorphic Functions. Philadelphia-London-Toronto: W.B. Saunders 1969
23. Katok, S.: Fuchsian Group. Chicago Lecture in Mathematics, 1992
24. Berry, M.V.: Proc. R. Soc. London A400, 229 (1985)
25. Hardy, G.H., Littlewood, J.E.: Acta Mathematica 44, 1 (1922)
26. Magnus, W.: Non-Euclidean Tesselations and their Groups. New York: Academic Press (1974)
27. Terras, A.: Harmonic Analysis on Symmetric Spaces and Applications. Berlin, Heidelberg, New York, Springer 1979
28. Sarnak, P.: J. Number Theory 15, 229 (1982)
29. Matthies, C., Steiner, F.: Phys. Rev. A44, R7877 (1991)
30. Huber, H.: Math. Ann. 138, 1 (1959)
31. Berry, M.V.: In: [4]
32. Bogomolny, E., Schmit, C.: Nonlinearity 6, 523 (1993)
33. Aurich, R., Sieber, M.: J. Phys. A27, 1967 (1994)
34. Karamata, J.: J. reine und angewandte Mathematik 164, 27 (1931)
35. Feller, W.: An Introduction to Probability Theory and its Applications, vol. 1, New-York: John Wiley and Sons, 1957; vol. 2, 1971
36. Feller, W.: An Introduction to Probability Theory and its Applications, vol. 1, New-York: John Wiley and Sons, 1957; vol. 2, 1971
37. Vinogradov, I.M.: An Introduction to the Theory of Numbers. Oxford, London, New-York, Paris: Pergamon Press, Paris 1961
38. Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers. (4th ed.) Oxford: Clarendon Press, 1959
39. Kloosterman, H.D.: Acta Math. 49, 407 (1926)
40. Weil, A.: Proc. Nat. Acad. Sci. USA 34, 204 (1948)
41. Kusnetsov, N.V.: J. Sov. Math. 29, 1131 (1985)
42. Venkov, A.B.: Spectral Theory of Automorphic Functions. Proc. Steklov Institute of Math. 4 (1982)
43. Bogomolny, E., Leboeuf, P.: Nonlinearity 7, 1155 (1994)
44. Titchmarsh, B.C.: The Theory of the Riemann Zeta-Function. Oxford: Clarendon Press, 1951
45. Rankin, R.A.: Modular Forms and Functions. Cambridge: Cambridge University Press, 1977