@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}, pages = {769--799}, publisher = {Elsevier}, volume = {Ser. 4, 37}, number = {5}, year = {2004}, doi = {10.1016/j.ansens.2004.08.001}, mrnumber = {2103474}, zbl = {02136290}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.ansens.2004.08.001/} }
TY - JOUR AU - Luo, Wenzhi AU - Sarnak, Peter TI - Quantum variance for Hecke eigenforms JO - Annales scientifiques de l'École Normale Supérieure PY - 2004 SP - 769 EP - 799 VL - 37 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.ansens.2004.08.001/ DO - 10.1016/j.ansens.2004.08.001 LA - en ID - ASENS_2004_4_37_5_769_0 ER -
%0 Journal Article %A Luo, Wenzhi %A Sarnak, Peter %T Quantum variance for Hecke eigenforms %J Annales scientifiques de l'École Normale Supérieure %D 2004 %P 769-799 %V 37 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.ansens.2004.08.001/ %R 10.1016/j.ansens.2004.08.001 %G en %F ASENS_2004_4_37_5_769_0
Luo, Wenzhi; Sarnak, Peter. Quantum variance for Hecke eigenforms. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 5, pp. 769-799. doi : 10.1016/j.ansens.2004.08.001. http://archive.numdam.org/articles/10.1016/j.ansens.2004.08.001/
[1] Automorphic Forms on , Lecture Notes in Mathematics, vol. 1083, Springer-Verlag, Berlin, 1984. | MR | Zbl
,[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 | Zbl
,[3] Kloosterman sum and Fourier coefficients of cusp forms, Invent. Math. 70 (1982) 219-288. | MR | Zbl
, ,[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
, ,[7] A relation between automorphic representations of and , Ann. Sci. École Norm. Sup. 11 (1978) 471-552. | Numdam | MR | Zbl
, ,[8] Tables of Integrals, Series and Products, Academic Press, New York, 1965. | MR | Zbl
, ,[9] Differential Geometry and Symmetric Spaces, Pure and Applied Mathematics, vol. XII, Academic Press, New York, 1962. | MR | Zbl
,[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 | Zbl
, ,[11] Introduction to the Spectral Theory of Automorphic Forms, Revista Matematica Iberoamericana, Madrid, 1995. | MR | Zbl
,[12] Topics in Classical Automorphic Forms, Graduate Studies in Mathematics, vol. 17, AMS, 1997. | MR | Zbl
,[13] Low lying zeros of families of L-functions, Inst. Hautes Études Sci. Publ. Math. 91 (2001) 55-131. | Numdam | MR | Zbl
, , ,[14] Perspectives on the analytic theory of L-functions, Geom. Funct. Anal. (2000) 705-741, Special Volume, Part II. | MR | Zbl
, ,[15] The nonvanishing of central values of automorphic L-functions and Siegel's zero, Israel J. Math. A 120 (2000) 155-177. | MR | Zbl
, ,[16] Equidistribution of cusp forms on , Ann. Inst. Fourier (Grenoble) 47 (3) (1997) 967-984. | Numdam | MR | Zbl
,[17] Heegner points, cycles and Maass forms, Israel J. Math. 84 (1993) 193-227. | MR | Zbl
, ,[18] Random Matrices, Frobenius Eigenvalues and Monodromy, Colloquium Publications, vol. 45, AMS, 1999. | MR | Zbl
, ,[19] Random matrix theory and L-functions at , Comm. Math. Phys. 214 (1) (2000) 91-110. | MR | Zbl
, ,[20] Kurlberg, P., Rudnick, Z., On the distribution of matrix elements for the quantum cat map, preprint, 2003. | MR
[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 | Zbl
,[22] Values of symmetric square L-functions at 1, J. Reine Angew. Math. 506 (1999) 215-235. | MR | Zbl
,[23] Quantum ergodicity of eigenfunctions on , Inst. Hautes Études Sci. Publ. Math. 81 (1995) 207-237. | Numdam | MR | Zbl
, ,[24] Mass equidistribution for Hecke eigenforms, Comm. Pure Appl. Math. 56 (7) (2003) 874-891. | MR | Zbl
, ,[25] The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature, Israel J. Math. 16 (1973) 181-197. | MR | Zbl
,[26] The rate of mixing for geodesic and horocycle flows, Ergodic Theory Dynam. Systems 7 (1987) 267-288. | MR | Zbl
,[27] Uber die Kloostermanschen Summen , Math. Z. 34 (1931) 91-109. | MR | Zbl
,[28] Sarnak, P., Arithmetic quantum chaos, The R.A. Blyth Lecture, University of Toronto, 1993. | MR
[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 | Zbl
,[31] Harmonic Analysis on Symmetric Spaces and Applications I, Springer-Verlag, New York, 1985. | MR | Zbl
,[32] Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55 (1987) 919-941. | MR | Zbl
,[33] On the rate of quantum ergodicity, I. Upper bounds, Comm. Math. Phys. 160 (1) (1994) 81-92. | MR | Zbl
,Cité par Sources :