Quantum ergodicity of Eigenfunctions on PSL 2 (𝐙)/𝐇 2
Publications Mathématiques de l'IHÉS, Tome 81 (1995), pp. 207-237.
@article{PMIHES_1995__81__207_0,
     author = {Luo, Wenzhi and Sarnak, Peter},
     title = {Quantum ergodicity of {Eigenfunctions} on $PSL_2(\mathbf {Z})/\mathbf {H}^2$},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {207--237},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {81},
     year = {1995},
     mrnumber = {1361757},
     zbl = {0852.11024},
     language = {en},
     url = {http://archive.numdam.org/item/PMIHES_1995__81__207_0/}
}
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Luo, Wenzhi; Sarnak, Peter. Quantum ergodicity of Eigenfunctions on $PSL_2(\mathbf {Z})/\mathbf {H}^2$. Publications Mathématiques de l'IHÉS, Tome 81 (1995), pp. 207-237. http://archive.numdam.org/item/PMIHES_1995__81__207_0/

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

[D-I1] J.-M Deshouillers, H. Iwaniec, Kloosterman sum and Fourier coefficients of cusp forms, Invent. Math., 70 (1982), 219-288. | MR | Zbl

[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. | MR | Zbl

[ER] A. Erdélyi et al., Higher Transcendental Functions, vol. 2, McGraw-Hill, 1953. | MR | Zbl

[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. | MR | Zbl

[H2] D. A. Hejhal, The Selberg Trace Formula for PSL(2, R), Vol. 2, Springer Lecture Notes, 1001, Springer-Verlag, 1983. | MR | Zbl

[H3] D. A. Hejhal, Eigenvalues for the Laplacian for Hecke triangle groups, Memoirs of AMS, Vol. 469, 1992. | Zbl

[H-R] D. A. Hejhal, D. Rackner, On the topography of Maass wave forms, Exper. Math., 1 (1992), 275-305. | Zbl

[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. | MR | Zbl

[I1] H. Iwaniec, Prime geodesic theorem, J. Reine Angew. Math., 349 (1984), 136-159. | MR | Zbl

[12] H. Iwaniec, Small eigenvalues for Γ0(N), Acta Arith., LVI (1990), 65-82. | MR | Zbl

[13] H. Iwaniec, The spectral growth of automorphic L-functions, J. Reine Angew. Math., 428 (1992), 139-159. | MR | Zbl

[I-S] H. Iwaniec, H. Sarnak, L∞ norms of eigenfunctions of arithmetic surfaces, To appear in Annals of Math. | Zbl

[14] H. Iwaniec, Non-holomorphic modular forms and their applications, Modular forms, Durham conference, edited by R. Rankin, 1984, 157-196. | MR | Zbl

[J] D. Jakobson, Quantum ergodicity for Eisenstein series on PSL2(Z)\PSL2(R), Preprint, Princeton, 1994. | Numdam | MR | Zbl

[K-N] L. Kuipers, H. Niederreiter, Uniform distribution of sequences, New York, Wiley, 1974. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[RA] S. Ramanujan, Some formulae in the arithmetic theory of numbers, Messenger of Math., 45 (1916), 81-84. | JFM

[RAN] B. Randol, On the asymptotic distribution of closed geodesics on compact Riemann surfaces, Trans. AMS, 233 (1977), 241-247. | MR | Zbl

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

[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. | MR | Zbl

[SE] A. Selberg, Collected Papers, Vol. 1, Springer-Verlag, 1989, 626-674. | MR | Zbl

[SH] A. I. Schnirelman, Ergodic properties of eigenfunctions, Usp. Math. Nauk., 29 (1974), 181-182. | MR

[SHI] G. Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. (3), 31 (1975), 79-98. | MR | Zbl

[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. | MR | Zbl

[W] A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. USA, 34 (1948), 204-207. | MR | Zbl

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

[Z2] S. Zelditch, Selberg trace formulae and equidistribution theorems, Memoirs of AMS, Vol. 96, No. 465, 1992. | MR | Zbl