@article{ASENS_2004_4_37_5_769_0,
author = {Luo, Wenzhi and Sarnak, Peter},
title = {Quantum variance for Hecke eigenforms},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
volume = {37},
year = {2004},
pages = {769-799},
doi = {10.1016/j.ansens.2004.08.001},
mrnumber = {2103474},
zbl = {02136290},
language = {en},
url = {http://dml.mathdoc.fr/item/ASENS_2004_4_37_5_769_0}
}
Luo, Wenzhi; Sarnak, Peter. Quantum variance for Hecke eigenforms. Annales scientifiques de l'École Normale Supérieure, Tome 37 (2004) pp. 769-799. doi : 10.1016/j.ansens.2004.08.001. http://gdmltest.u-ga.fr/item/ASENS_2004_4_37_5_769_0/
[1] , Automorphic Forms on , Lecture Notes in Mathematics, vol. 1083, Springer-Verlag, Berlin, 1984. | MR 765698 | Zbl 0543.22005
[2] , The Rankin-Selberg method: a survey, in: Number Theory, Trace Formulas and Discrete Groups (Oslo, 1987), Academic Press, Boston, MA, 1989, pp. 49-109. | MR 993311 | Zbl 0668.10034
[3] , , Kloosterman sum and Fourier coefficients of cusp forms, Invent. Math. 70 (1982) 219-288. | MR 684172 | Zbl 0502.10021
[4] Miller, S., Dueñez, E., The low-lying zeros of a family of L-functions, preprint, 2004.
[5] , , , , , , Approach to ergodicity in quantum wave functions, Phys. Rev. E 52 (1995) 5893-5903.
[6] , , Distribution of matrix elements of chaotic systems, Phys. Rev. A (3) 34 (1) (1986) 591-595. | MR 848319
[7] , , A relation between automorphic representations of and , Ann. Sci. École Norm. Sup. 11 (1978) 471-552. | Numdam | MR 533066 | Zbl 0406.10022
[8] , , Tables of Integrals, Series and Products, Academic Press, New York, 1965. | MR 1773820 | Zbl 0918.65002
[9] , Differential Geometry and Symmetric Spaces, Pure and Applied Mathematics, vol. XII, Academic Press, New York, 1962. | MR 145455 | Zbl 0111.18101
[10] , , Coefficients of Maass forms and the Siegel zero, appendix by Goldfeld, D., Hoffstein, J., Lieman, D. An effective zero free region, Annals of Math. 140 (1994) 161-181. | MR 1289494 | Zbl 0814.11032
[11] , Introduction to the Spectral Theory of Automorphic Forms, Revista Matematica Iberoamericana, Madrid, 1995. | MR 1325466 | Zbl 0847.11028
[12] , Topics in Classical Automorphic Forms, Graduate Studies in Mathematics, vol. 17, AMS, 1997. | MR 1474964 | Zbl 0905.11023
[13] , , , Low lying zeros of families of L-functions, Inst. Hautes Études Sci. Publ. Math. 91 (2001) 55-131. | Numdam | MR 1828743 | Zbl 1012.11041
[14] , , Perspectives on the analytic theory of L-functions, Geom. Funct. Anal. (2000) 705-741, Special Volume, Part II. | MR 1826269 | Zbl 0996.11036
[15] , , The nonvanishing of central values of automorphic L-functions and Siegel's zero, Israel J. Math. A 120 (2000) 155-177. | MR 1815374 | Zbl 0992.11037
[16] , Equidistribution of cusp forms on , Ann. Inst. Fourier (Grenoble) 47 (3) (1997) 967-984. | Numdam | MR 1465794 | Zbl 0868.43011
[17] , , Heegner points, cycles and Maass forms, Israel J. Math. 84 (1993) 193-227. | MR 1244668 | Zbl 0787.11016
[18] , , Random Matrices, Frobenius Eigenvalues and Monodromy, Colloquium Publications, vol. 45, AMS, 1999. | MR 1659828 | Zbl 0958.11004
[19] , , Random matrix theory and L-functions at , Comm. Math. Phys. 214 (1) (2000) 91-110. | MR 1794267 | Zbl 1051.11047
[20] Kurlberg, P., Rudnick, Z., On the distribution of matrix elements for the quantum cat map, preprint, 2003. | MR 2150390
[21] , Petersson's conjecture for cusp forms of weight zero and Linnik's conjecture, sums of Kloosterman sums, Mat. Sb. 111 (1980) 334-383. | MR 568983 | Zbl 0427.10016
[22] , Values of symmetric square L-functions at 1, J. Reine Angew. Math. 506 (1999) 215-235. | MR 1665705 | Zbl 0969.11018
[23] , , Quantum ergodicity of eigenfunctions on , Inst. Hautes Études Sci. Publ. Math. 81 (1995) 207-237. | Numdam | MR 1361757 | Zbl 0852.11024
[24] , , Mass equidistribution for Hecke eigenforms, Comm. Pure Appl. Math. 56 (7) (2003) 874-891. | MR 1990480 | Zbl 1044.11022
[25] , The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature, Israel J. Math. 16 (1973) 181-197. | MR 333121 | Zbl 0283.58010
[26] , The rate of mixing for geodesic and horocycle flows, Ergodic Theory Dynam. Systems 7 (1987) 267-288. | MR 896798 | Zbl 0623.22008
[27] , Uber die Kloostermanschen Summen , Math. Z. 34 (1931) 91-109. | MR 1545243 | Zbl 0002.12801
[28] Sarnak, P., Arithmetic quantum chaos, The R.A. Blyth Lecture, University of Toronto, 1993. | MR 1321639
[29] Watson, T., Rankin triple products and quantum chaos, Thesis, Princeton University, 2001.
[30] , A Course in Arithmetic, Graduate Texts in Mathematics, vol. 7, Springer-Verlag, New York, 1973. | MR 344216 | Zbl 0256.12001
[31] , Harmonic Analysis on Symmetric Spaces and Applications I, Springer-Verlag, New York, 1985. | MR 791406 | Zbl 0574.10029
[32] , Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55 (1987) 919-941. | MR 916129 | Zbl 0643.58029
[33] , On the rate of quantum ergodicity, I. Upper bounds, Comm. Math. Phys. 160 (1) (1994) 81-92. | MR 1262192 | Zbl 0788.58043