Recherche et téléchargement d’archives de revues mathématiques numérisées

 
 
  Table des matières de ce fascicule | Article précédent | Article suivant
Hejhal, Dennis A.
Eigenfunctions of the laplacian, quantum chaos, and computation. Journées équations aux dérivées partielles (1995), Art. No. 7, 11 p.
Texte intégral djvu | pdf | Analyses MR 1360476 | Zbl 0948.35507

URL stable: http://www.numdam.org/item?id=JEDP_1995____A7_0

Bibliographie

[B] M. Berry, Regular and irregular semiclassical wavefunctions, J. Phys. A10 (1977) 2083-2091.  MR 58 #8961 |  Zbl 0377.70014
[C] Y. Colin de Verdiere, Ergodicité et fonctions propres du laplacien, Comm. Math. Phys. 102 (1985) 497-502.
Article |  MR 87d:58145 |  Zbl 0592.58050
[D] P. Deligne, La conjecture de Weil I, IHES Publ. Math. 53 (1974) 273-307.
Numdam |  MR 49 #5013 |  Zbl 0287.14001
[G] A. Good, Cusp forms and eigenfunctions of the Laplacian, Math. Ann. 255 (1981) 523-548.  MR 82i:10029 |  Zbl 0439.30031
[H1] D.A. Hejhal, The Selberg Trace Formula for PSL (2,ℝ), vol. 1, Springer Lecture Notes in Mathematics 548 (1976), 516 pp.  MR 55 #12641 |  Zbl 0347.10018
[H2] D.A. Hejhal, The Selberg Trace Formula for PSL (2,ℝ), vol. 2, Springer Lecture Notes in Mathematics 1001 (1983), 806 pp.  MR 86e:11040 |  Zbl 0543.10020
[H3] D.A. Hejhal, Eigenvalues of the Laplacian for Hecke triangle groups, American Math. Soc. Memoir 469 (1992), 165 pp.  Zbl 0746.11025
[HA] D.A. Hejhal and S. Arno, On Fourier coefficients of Maass waveforms for PSL (2,ℤ), Math. of Comp. 61 (1993) 245-267 and S11-S16.  MR 94a:11062 |  Zbl 0781.11020
[HR] D.A. Hejhal and B. Rackner, On the topography of Maass waveforms for PSL (2,ℤ), Experimental Math. 1 (1992) 275-305.
Article |  MR 95f:11037 |  Zbl 0813.11035
[L] D.H. Lehmer, Note on the distribution of Ramanujan's tau function, Math. of Comp. 24 (1970) 741-743.  MR 43 #166 |  Zbl 0214.30601
[LS] W. Luo and P. Sarnak, Quantum ergodicity of eigenfunctions on PSL (2,ℤ) \ H, preprint, 1995, 38 pp.
Numdam |  MR 97f:11037 |  Zbl 0852.11024
[MS] C. Moreno and F. Shahidi, The fourth moment of Ramanujan's τ - function, Math. Ann. 266 (1983) 233-239.  MR 85i:11039 |  Zbl 0508.10014
[P] Y. Petridis, On squares of eigenfunctions for the hyperbolic plane and a new bound on certain L-series, International Math. Res. Notices (1995) 111-127.  MR 96d:11058 |  Zbl 0833.11021
[PS] R. Phillips and P. Sarnak, On cusp forms for cofinite subgroups of PSL (2,ℝ), Invent. Math. 80 (1985) 339-364.  MR 86m:11037 |  Zbl 0558.10017
[R1] R.A. Rankin, Sums of powers of cusp form coefficients II, Math. Ann. 272 (1985) 593-600.  MR 87d:11032 |  Zbl 0556.10018
[R2] R.A. Rankin, A family of newforms, Ann. Acad. Sci. Fennicae 10 (1985) 461-467.  MR 87b:11036 |  Zbl 0595.10019
[R3] R.A. Rankin, Fourier coefficients of cusp forms, Math. Proc. Cambr. Phil. Soc. 100 (1986) 5-29, especially 26-27.  MR 87i:11060 |  Zbl 0616.10020
[Ra] M. Ratner, The rate of mixing for geodesic and horocycle flows, Ergodic Th. and Dyn. Sys. 7 (1987) 267-288.  MR 88j:58103 |  Zbl 0623.22008
[Re] F. Reza, An Introduction to Information Theory, Dover Publications, 1994, especially §§8.6 and 8.7.  MR 1298628 |  Zbl 0925.94068
[RS] Z. Rudnick and P. Sarnak, The behavior of eigenstates of arithmetic hyperbolic manifolds, Comm. Math. Phys. 161 (1994) 195-213.
Article |  MR 95m:11052 |  Zbl 0836.58043
[S1] P. Sarnak, Asymptotic behavior of periodic orbits of the horocyclic flow and Eisenstein series, Comm. Pure Appl. Math. 34 (1981) 719-739.  MR 83m:58060 |  Zbl 0501.58027
[S2] P. Sarnak, On cusp forms, American Math. Soc. Contemp. Math. 53 (1986) 393-407.  MR 87j:11047 |  Zbl 0618.10018
[S3] P. Sarnak, Inner products of eigenfunctions, International Math. Res. Notices (1994) 251-260.  MR 95i:11039 |  Zbl 0833.11020
[ShW] C. Shannon and W. Weaver, The Mathematical Theory of Communication, Univ. of I11. Press, 1949, especially pp. 55, 56.  MR 11,258e |  Zbl 0041.25804
[Sh1] A. Shnirelman, Ergodic properties of eigenfunctions, Uspekhi Mat. Nauk. 29 (6) (1974) 181-182 [in Russian].  MR 53 #6648
[Sh2] A. Shnirelman, On the asymptotic properties of eigenfunctions in the regions of chaotic motion, Addendum in the book : V.F. Lazutkin, KAM Theory and Semiclassical Asymptotics to Eigenfunctions, Springer-Verlag, 1993, pp. 313-337.
[St] G. Steil, Eigenvalues of the Laplacian and of the Hecke operators for PSL (2,ℤ), Hamburg DESY Preprint 94-028, 1994, 25 pp.
[T] J. Thomas, An Introduction to Statistical Communication Theory, Wiley, 1969, especially pages 481 (top), 561, 562.  Zbl 0202.17801
[V] A. Venkov, Spectral Theory of Automorphic Functions, Proc. Steklov Inst. Math. 153 (1982) 163 pp.  MR 85j:11060b |  Zbl 0501.10029
[Z1] S. Zelditch, Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55 (1987) 919-941.
Article |  MR 89d:58129 |  Zbl 0643.58029
[Z2] S. Zelditch, Mean Lindelöf hypothesis and equidistribution of cusp forms and Eisenstein series, J. Funct. Anal. 97 (1991) 1-49.  MR 92h:11046 |  Zbl 0743.58034
Copyright Cellule MathDoc 2014 | Crédit | Plan du site