@article{JEDP_1995____A7_0,
author = {Hejhal, Dennis A.},
title = {Eigenfunctions of the laplacian, quantum chaos, and computation},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
year = {1995},
pages = {1-11},
mrnumber = {1360476},
zbl = {0948.35507},
language = {en},
url = {http://dml.mathdoc.fr/item/JEDP_1995____A7_0}
}
Hejhal, Dennis A. Eigenfunctions of the laplacian, quantum chaos, and computation. Journées équations aux dérivées partielles, (1995), pp. 1-11. http://gdmltest.u-ga.fr/item/JEDP_1995____A7_0/
[B] , Regular and irregular semiclassical wavefunctions, J. Phys. A10 (1977) 2083-2091. | MR 58 #8961 | Zbl 0377.70014
[C] , Ergodicité et fonctions propres du laplacien, Comm. Math. Phys. 102 (1985) 497-502. | MR 87d:58145 | Zbl 0592.58050
[D] , La conjecture de Weil I, IHES Publ. Math. 53 (1974) 273-307. | Numdam | MR 49 #5013 | Zbl 0287.14001
[G] , Cusp forms and eigenfunctions of the Laplacian, Math. Ann. 255 (1981) 523-548. | MR 82i:10029 | Zbl 0439.30031
[H1] , 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] , 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] , Eigenvalues of the Laplacian for Hecke triangle groups, American Math. Soc. Memoir 469 (1992), 165 pp. | Zbl 0746.11025
[HA] and , 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] and , On the topography of Maass waveforms for PSL (2,ℤ), Experimental Math. 1 (1992) 275-305. | MR 95f:11037 | Zbl 0813.11035
[L] , Note on the distribution of Ramanujan's tau function, Math. of Comp. 24 (1970) 741-743. | MR 43 #166 | Zbl 0214.30601
[LS] and , Quantum ergodicity of eigenfunctions on PSL (2,ℤ) \ H1995, 38 pp. | Numdam | MR 97f:11037 | Zbl 0852.11024
[MS] and , The fourth moment of Ramanujan's τ - function, Math. Ann. 266 (1983) 233-239. | MR 85i:11039 | Zbl 0508.10014
[P] , 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] and , On cusp forms for cofinite subgroups of PSL (2,ℝ), Invent. Math. 80 (1985) 339-364. | MR 86m:11037 | Zbl 0558.10017
[R1] , Sums of powers of cusp form coefficients II, Math. Ann. 272 (1985) 593-600. | MR 87d:11032 | Zbl 0556.10018
[R2] , A family of newforms, Ann. Acad. Sci. Fennicae 10 (1985) 461-467. | MR 87b:11036 | Zbl 0595.10019
[R3] , Fourier coefficients of cusp forms, Math. Proc. Cambr. Phil. Soc. 100 (1986) 5-29, especially 26-27. | MR 87i:11060 | Zbl 0616.10020
[Ra] , 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] , An Introduction to Information Theory, Dover Publications, 1994, especially §§8.6 and 8.7. | MR 1298628 | Zbl 0925.94068
[RS] and , The behavior of eigenstates of arithmetic hyperbolic manifolds, Comm. Math. Phys. 161 (1994) 195-213. | MR 95m:11052 | Zbl 0836.58043
[S1] , 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] , On cusp forms, American Math. Soc. Contemp. Math. 53 (1986) 393-407. | MR 87j:11047 | Zbl 0618.10018
[S3] , Inner products of eigenfunctions, International Math. Res. Notices (1994) 251-260. | MR 95i:11039 | Zbl 0833.11020
[ShW] and , The Mathematical Theory of Communication, Univ. of I11. Press, 1949, especially pp. 55, 56. | MR 11,258e | Zbl 0041.25804
[Sh1] , Ergodic properties of eigenfunctions, Uspekhi Mat. Nauk. 29 (6) (1974) 181-182 [in Russian]. | MR 53 #6648
[Sh2] , 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] , Eigenvalues of the Laplacian and of the Hecke operators for PSL (2,ℤ), Hamburg DESY Preprint 94-028, 1994, 25 pp.
[T] , An Introduction to Statistical Communication Theory, Wiley, 1969, especially pages 481 (top), 561, 562. | Zbl 0202.17801
[V] , Spectral Theory of Automorphic Functions, Proc. Steklov Inst. Math. 153 (1982) 163 pp. | MR 85j:11060b | Zbl 0501.10029
[Z1] , Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55 (1987) 919-941. | MR 89d:58129 | Zbl 0643.58029
[Z2] , Mean Lindelöf hypothesis and equidistribution of cusp forms and Eisenstein series, J. Funct. Anal. 97 (1991) 1-49. | MR 92h:11046 | Zbl 0743.58034