Eigenfunctions of the laplacian, quantum chaos, and computation
Journées équations aux dérivées partielles (1995), article no. 7, 11 p.
Dennis A. Hejhal. Eigenfunctions of the laplacian, quantum chaos, and computation. Journées équations aux dérivées partielles (1995), article  no. 7, 11 p.. doi: 10.5802/jedp.479
@incollection{JEDP_1995____A7_0,
     author = {Dennis A. Hejhal},
     title = {Eigenfunctions of the laplacian, quantum chaos, and computation},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {7},
     pages = {1--11},
     year = {1995},
     publisher = {\'Ecole polytechnique},
     doi = {10.5802/jedp.479},
     mrnumber = {1360476},
     zbl = {0948.35507},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.479/}
}
TY  - JOUR
AU  - Dennis A. Hejhal
TI  - Eigenfunctions of the laplacian, quantum chaos, and computation
JO  - Journées équations aux dérivées partielles
PY  - 1995
SP  - 1
EP  - 11
PB  - École polytechnique
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.479/
DO  - 10.5802/jedp.479
LA  - en
ID  - JEDP_1995____A7_0
ER  - 
%0 Journal Article
%A Dennis A. Hejhal
%T Eigenfunctions of the laplacian, quantum chaos, and computation
%J Journées équations aux dérivées partielles
%] 7
%D 1995
%P 1-11
%I École polytechnique
%U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.479/
%R 10.5802/jedp.479
%G en
%F JEDP_1995____A7_0

[B] M. Berry, Regular and irregular semiclassical wavefunctions, J. Phys. A10 (1977) 2083-2091. | MR | Zbl

[C] Y. Colin De Verdiere, Ergodicité et fonctions propres du laplacien, Comm. Math. Phys. 102 (1985) 497-502. | MR | Zbl

[D] P. Deligne, La conjecture de Weil I, IHES Publ. Math. 53 (1974) 273-307. | Numdam | MR | Zbl

[G] A. Good, Cusp forms and eigenfunctions of the Laplacian, Math. Ann. 255 (1981) 523-548. | MR | Zbl

[H1] D.A. Hejhal, The Selberg Trace Formula for PSL (2,ℝ), vol. 1, Springer Lecture Notes in Mathematics 548 (1976), 516 pp. | MR | Zbl

[H2] D.A. Hejhal, The Selberg Trace Formula for PSL (2,ℝ), vol. 2, Springer Lecture Notes in Mathematics 1001 (1983), 806 pp. | MR | Zbl

[H3] D.A. Hejhal, Eigenvalues of the Laplacian for Hecke triangle groups, American Math. Soc. Memoir 469 (1992), 165 pp. | Zbl

[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 | Zbl

[HR] D.A. Hejhal and B. Rackner, On the topography of Maass waveforms for PSL (2,ℤ), Experimental Math. 1 (1992) 275-305. | MR | Zbl

[L] D.H. Lehmer, Note on the distribution of Ramanujan's tau function, Math. of Comp. 24 (1970) 741-743. | MR | Zbl

[LS] W. Luo and P. Sarnak, Quantum ergodicity of eigenfunctions on PSL (2,ℤ) \ H1995, 38 pp. | Numdam | MR | Zbl

[MS] C. Moreno and F. Shahidi, The fourth moment of Ramanujan's τ - function, Math. Ann. 266 (1983) 233-239. | MR | Zbl

[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 | Zbl

[PS] R. Phillips and P. Sarnak, On cusp forms for cofinite subgroups of PSL (2,ℝ), Invent. Math. 80 (1985) 339-364. | MR | Zbl

[R1] R.A. Rankin, Sums of powers of cusp form coefficients II, Math. Ann. 272 (1985) 593-600. | MR | Zbl

[R2] R.A. Rankin, A family of newforms, Ann. Acad. Sci. Fennicae 10 (1985) 461-467. | MR | Zbl

[R3] R.A. Rankin, Fourier coefficients of cusp forms, Math. Proc. Cambr. Phil. Soc. 100 (1986) 5-29, especially 26-27. | MR | Zbl

[Ra] M. Ratner, The rate of mixing for geodesic and horocycle flows, Ergodic Th. and Dyn. Sys. 7 (1987) 267-288. | MR | Zbl

[Re] F. Reza, An Introduction to Information Theory, Dover Publications, 1994, especially §§8.6 and 8.7. | MR | Zbl

[RS] Z. Rudnick and P. Sarnak, The behavior of eigenstates of arithmetic hyperbolic manifolds, Comm. Math. Phys. 161 (1994) 195-213. | MR | Zbl

[S1] P. Sarnak, Asymptotic behavior of periodic orbits of the horocyclic flow and Eisenstein series, Comm. Pure Appl. Math. 34 (1981) 719-739. | MR | Zbl

[S2] P. Sarnak, On cusp forms, American Math. Soc. Contemp. Math. 53 (1986) 393-407. | MR | Zbl

[S3] P. Sarnak, Inner products of eigenfunctions, International Math. Res. Notices (1994) 251-260. | MR | Zbl

[ShW] C. Shannon and W. Weaver, The Mathematical Theory of Communication, Univ. of I11. Press, 1949, especially pp. 55, 56. | MR | Zbl

[Sh1] A. Shnirelman, Ergodic properties of eigenfunctions, Uspekhi Mat. Nauk. 29 (6) (1974) 181-182 [in Russian]. | MR

[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

[V] A. Venkov, Spectral Theory of Automorphic Functions, Proc. Steklov Inst. Math. 153 (1982) 163 pp. | MR | Zbl

[Z1] S. Zelditch, Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55 (1987) 919-941. | MR | Zbl

[Z2] S. Zelditch, Mean Lindelöf hypothesis and equidistribution of cusp forms and Eisenstein series, J. Funct. Anal. 97 (1991) 1-49. | MR | Zbl

Cited by Sources: