Quantum ergodicity of Eigenfunctions on
Publications Mathématiques de l'IHÉS (1995)
- Volume: 81, page 207-237
- ISSN: 0073-8301
Access Full Article
topHow to cite
topLuo, Wenzhi, and Sarnak, Peter. "Quantum ergodicity of Eigenfunctions on $PSL_2(\mathbf {Z})/\mathbf {H}^2$." Publications Mathématiques de l'IHÉS 81 (1995): 207-237. <http://eudml.org/doc/104103>.
@article{Luo1995,
author = {Luo, Wenzhi, Sarnak, Peter},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {quantum ergodicity of eigenfunctions; Maass cusp form; Eisenstein series; prime geodesic theorem; modular forms; -functions; Fourier coefficients},
language = {eng},
pages = {207-237},
publisher = {Institut des Hautes Études Scientifiques},
title = {Quantum ergodicity of Eigenfunctions on $PSL_2(\mathbf \{Z\})/\mathbf \{H\}^2$},
url = {http://eudml.org/doc/104103},
volume = {81},
year = {1995},
}
TY - JOUR
AU - Luo, Wenzhi
AU - Sarnak, Peter
TI - Quantum ergodicity of Eigenfunctions on $PSL_2(\mathbf {Z})/\mathbf {H}^2$
JO - Publications Mathématiques de l'IHÉS
PY - 1995
PB - Institut des Hautes Études Scientifiques
VL - 81
SP - 207
EP - 237
LA - eng
KW - quantum ergodicity of eigenfunctions; Maass cusp form; Eisenstein series; prime geodesic theorem; modular forms; -functions; Fourier coefficients
UR - http://eudml.org/doc/104103
ER -
References
top- [CD] Y. COLIN DE VERDIÈRE, Ergodicité et fonctions propres du laplacien, Com. Math. Phys., 102 (1985), 497-502. Zbl0592.58050MR87d:58145
- [D-I1] J.-M DESHOUILLERS, H. IWANIEC, Kloosterman sum and Fourier coefficients of cusp forms, Invent. Math., 70 (1982), 219-288. Zbl0502.10021MR84m:10015
- [D-12] J.-M. DESHOUILLERS, H. IWANIEC, The non-vanishing of Rankin-Selberg zeta-functions at special points, Selberg trace formula and related topics, Contemp. Math., 53, Amer. Math. Soc., Providence, RI, 1986, 59-95. Zbl0595.10025MR88d:11047
- [ER] A. ERDÉLYI et al., Higher Transcendental Functions, vol. 2, McGraw-Hill, 1953. Zbl0051.30303MR15,419i
- [G-R] I. S. GRADSHTEIN, I. M. RYZHIK, Tables of Integrals, Series and Products, Academic Press, New York and London, 1965.
- [H1] D. A. HEJHAL, The Selberg Trace Formula for PSL(2, R), Vol. 1, Springer Lecture Notes, 548, Springer-Verlag, 1976. Zbl0347.10018MR55 #12641
- [H2] D. A. HEJHAL, The Selberg Trace Formula for PSL(2, R), Vol. 2, Springer Lecture Notes, 1001, Springer-Verlag, 1983. Zbl0543.10020MR86e:11040
- [H3] D. A. HEJHAL, Eigenvalues for the Laplacian for Hecke triangle groups, Memoirs of AMS, Vol. 469, 1992. Zbl0746.11025
- [H-R] D. A. HEJHAL, D. RACKNER, On the topography of Maass wave forms, Exper. Math., 1 (1992), 275-305. Zbl0813.11035
- [HN-L] J. HOFFSTEIN, P. LOCKHART, Coefficients of Maass forms and the Siegel zero, appendix by D. Goldfeld, J. Hoffstein, D. Lieman, An affective zero free region, Annals of Math., 140 (1994), 161-181. Zbl0814.11032MR95m:11048
- [I1] H. IWANIEC, Prime geodesic theorem, J. Reine Angew. Math., 349 (1984), 136-159. Zbl0527.10021MR85h:11025
- [12] H. IWANIEC, Small eigenvalues for Γ0(N), Acta Arith., LVI (1990), 65-82. Zbl0702.11034MR92h:11045
- [13] H. IWANIEC, The spectral growth of automorphic L-functions, J. Reine Angew. Math., 428 (1992), 139-159. Zbl0746.11024MR93g:11049
- [I-S] H. IWANIEC, H. SARNAK, L∞ norms of eigenfunctions of arithmetic surfaces, To appear in Annals of Math. Zbl0833.11019
- [14] H. IWANIEC, Non-holomorphic modular forms and their applications, Modular forms, Durham conference, edited by R. Rankin, 1984, 157-196. Zbl0558.10018MR87f:11030
- [J] D. JAKOBSON, Quantum ergodicity for Eisenstein series on PSL2(Z)2(R), Preprint, Princeton, 1994. Zbl0820.11040MR96b:11068
- [K-N] L. KUIPERS, H. NIEDERREITER, Uniform distribution of sequences, New York, Wiley, 1974. Zbl0281.10001MR54 #7415
- [KU] N. V. KUZNETSOV, Petersson's conjecture for cusp forms of weight zero and Linnik's conjecture, Sums of Kloosterman sums, Mat. Sb., 111 (1980), 334-383. Zbl0427.10016MR81m:10053
- [MEU] T. MEURMAN, On the order of the Maass L-function on the critical line, Number Theory, Vol. I, Budapest, 1987, Colloq. Math. Soc. Janos Bolyai, 51 (1990), 325-354. Zbl0724.11029MR91m:11037
- [RA] S. RAMANUJAN, Some formulae in the arithmetic theory of numbers, Messenger of Math., 45 (1916), 81-84. JFM45.1250.01
- [RAN] B. RANDOL, On the asymptotic distribution of closed geodesics on compact Riemann surfaces, Trans. AMS, 233 (1977), 241-247. Zbl0329.30009MR58 #2643
- [R-S] Z. RUDNICK, P. SARNAK, The behavior of eigenstates of arithmetic hyperbolic manifolds, Com. Math. Phys., 161 (1994), 195-213. Zbl0836.58043MR95m:11052
- [SA1] P. SARNAK, Arithmetic quantum chaos, The RA Blyth Lecture, University of Toronto, 1993.
- [SA2] P. SARNAK, Some Applications of modular forms, Cambridge Univ. Press, 1990. Zbl0721.11015MR92k:11045
- [SE] A. SELBERG, Collected Papers, Vol. 1, Springer-Verlag, 1989, 626-674. Zbl0675.10001MR92h:01083
- [SH] A. I. SCHNIRELMAN, Ergodic properties of eigenfunctions, Usp. Math. Nauk., 29 (1974), 181-182. MR53 #6648
- [SHI] G. SHIMURA, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. (3), 31 (1975), 79-98. Zbl0311.10029MR52 #3064
- [ST] G. STEIL, Über die Eigenwerte des Laplace Operators und die Hecke Operatoren für SL(2, Z), preprint, 1993.
- [T] E. C. TITCHMARSH, The Theory of the Riemann Zeta Function, Oxford, 1951. Zbl0042.07901MR13,741c
- [W] A. WEIL, On some exponential sums, Proc. Nat. Acad. Sci. USA, 34 (1948), 204-207. Zbl0032.26102MR10,234e
- [Z1] S. ZELDITCH, Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. Jnl., 55 (1987), 919-941. Zbl0643.58029MR89d:58129
- [Z2] S. ZELDITCH, Selberg trace formulae and equidistribution theorems, Memoirs of AMS, Vol. 96, No. 465, 1992. Zbl0753.11023MR93a:11047
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.