Équidistribution des orbites toriques sur les espaces homogènes [d'après M. Einsiedler, E. Lindenstrauss, Ph. Michel, A. Venkatesh]
Séminaire Bourbaki : volume 2008/2009 exposés 997-1011 - Avec table par noms d'auteurs de 1848/49 à 2008/09, Astérisque, no. 332 (2010), Exposé no. 1008, 35 p.
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     author = {Breuillard, Emmanuel},
     title = {\'Equidistribution des orbites toriques sur les espaces homog\`enes [d'apr\`es M. Einsiedler, E. Lindenstrauss, Ph. Michel, A. Venkatesh]},
     booktitle = {S\'eminaire Bourbaki : volume 2008/2009 expos\'es 997-1011  - Avec table par noms d'auteurs de 1848/49 \`a 2008/09},
     author = {Collectif},
     series = {Ast\'erisque},
     note = {talk:1008},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {332},
     year = {2010},
     zbl = {1209.22005},
     language = {fr},
     url = {http://archive.numdam.org/item/AST_2010__332__305_0/}
}
Breuillard, Emmanuel. Équidistribution des orbites toriques sur les espaces homogènes [d'après M. Einsiedler, E. Lindenstrauss, Ph. Michel, A. Venkatesh], dans Séminaire Bourbaki : volume 2008/2009 exposés 997-1011  - Avec table par noms d'auteurs de 1848/49 à 2008/09, Astérisque, no. 332 (2010), Exposé no. 1008, 35 p. http://archive.numdam.org/item/AST_2010__332__305_0/

[1] Y. Benoist & H. Oh - Equidistribution of rational matrices in their conjugacy classes, Geom. Fund. Anal. 17 (2007), p. 1-32. | Article | Zbl 1138.37003

[2] Y. Benoist & H. Oh, Effective equidistribution of S-integral points on symmetric varieties, prépublication arXiv:0706.1621. | Article | Numdam | Zbl 1330.11044

[3] N. Bergeron - Spectre des surfaces hyperboliques, livre en préparation. | Zbl 1267.11001

[4] V. Blomer, G. Harcos & P. Michel - Bounds for modular L-functions in the level aspect, Ann. Sci. École Norm. Sup. 40 (2007), p. 697-740. | Article | EuDML 82724 | Zbl 1185.11034

[5] A. Borel - Introduction aux groupes arithmétiques, Publications de l'Institut de Mathématique de l'Université de Strasbourg, XV. Actualités Scientifiques et Industrielles, No. 1341, Hermann, 1969. | Zbl 0186.33202

[6] R. Bowen - Periodic orbits for hyperbolic flows, Amer. J. Math. 94 (1972), p. 1-30. | Article | Zbl 0254.58005

[7] D. A. Burgess - On character sums and L-series. II, Proc. London Math. Soc. 13 (1963), p. 524-536. | Article | Zbl 0123.04404

[8] J. W. S. Cassels - The product of n inhomogeneous linear forms, J. London Math. Soc. (1952). | Zbl 0047.04902

[9] J. W. S. Cassels & H. P. F. Swinnerton-Dyer - On the product of three homogeneous linear forms and the indefinite ternary quadratic forms, Philos. Trans. Roy. Soc. London. Ser. A. 248 (1955), p. 73-96. | Article | Zbl 0065.27905

[10] L. Clozel & E. Ullmo - Équidistribution de mesures algébriques, Compos. Math. 141 (2005), p. 1255-1309. | Article | Zbl 1077.22014

[11] L. Clozel & E. Ullmo, Équidistribution de sous-variétés spéciales, Ann. of Math. 161 (2005), p. 1571-1588. | Article | Zbl 1099.11031

[12] P. B. Cohen - Hyperbolic equidistribution problems on Siegel 3-folds and Hilbert modular varieties, Duke Math. J. 129 (2005), p. 87-127. | Article | Zbl 1155.11326

[13] S. G. Dani & G. A. Margulis - Limit distributions of orbits of unipotent flows and values of quadratic forms, in I.M. Gel'fand Seminar, Adv. Soviet Math., vol. 16, Amer. Math. Soc., 1993, p. 91-137. | Article | Zbl 0814.22003

[14] W. Duke - Hyperbolic distribution problems and half-integral weight Maass forms, Invent. Math. 92 (1988), p. 73-90. | Article | EuDML 143559 | Zbl 0628.10029

[15] W. Duke, J. B. Friedlander & H. Iwaniec - Bounds for automorphic L-functions, Invent Math. 112 (1993), p. 1-8. | Article | EuDML 144092 | Zbl 0765.11038

[16] W. Duke, J. B. Friedlander & H. Iwaniec, The subconvexity problem for Artin L-functions, Invent. Math. 149 (2002), p. 489-577. | Article | Zbl 1056.11072

[17] M. Einsiedler - A simplified proof of Ratner's measure classification for the action of subgroups isomorphic to SL(2,), prépublication, 2008.

[18] M. Einsiedler & A. Katok - Invariant measures on G/Γ for split simple Lie groups G, Comm. Pure Appl. Math. 56 (2003), p. 1184-1221. | Article | Zbl 1022.22023

[19] M. Einsiedler & A. Katok, Rigidity of measures-the high entropy case and non-commuting foliations, Israel J. Math. 148 (2005), p. 169-238. | Article | Zbl 1097.37017

[20] M. Einsiedler, A. Katok & E. Lindenstrauss - Invariant measures and the set of exceptions to Littlewood's conjecture, Ann. of Math. 164 (2006), p. 513-560. | Article | MR 2247967 | Zbl 1109.22004

[21] M. Einsiedler & E. Lindenstrauss - Diagonalizable flows on locally homogeneous spaces and number theory, in Proceedings of the International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zurich, 2006, p. 1731-1759. | MR 2275667 | Zbl 1121.37028

[22] M. Einsiedler, E. Lindenstrauss P. Michel & A. Venkatesh, - Distribution of periodic torus orbits on homogeneous spaces I, Duke Math. J. 148 (2009), p. 119-174. | Article | MR 2515103 | Zbl 1172.37003

[23] M. Einsiedler, E. Lindenstrauss P. Michel & A. Venkatesh, Distribution of periodic torus orbits on homogeneous spaces II : Duke's theorem for quadratic fields, en préparation. | MR 2515103 | Zbl 1172.37003

[24] M. Einsiedler, E. Lindenstrauss P. Michel & A. Venkatesh, Distribution of periodic torus orbits on homogeneous spaces III : Duke's theorem for cubic fields, preprint, arXiv:math.0708.1113. | MR 2515103 | Zbl 1172.37003

[25] M. Einsiedler & T. Ward - Ergodic theory with a view towards number theory, livre à paraître dans la collection Springer Graduate Texts in Math. | MR 2723325 | Zbl 1206.37001

[26] A. Eskin - Counting problems and semisimple groups, in Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), 1998, p. 539-552. | EuDML 230497 | MR 1648103 | Zbl 0901.11029

[27] A. Eskin & C. Mcmullen - Mixing, counting, and equidistribution in Lie groups, Duke Math. J. 71 (1993), p. 181-209. | Article | MR 1230290 | Zbl 0798.11025

[28] A. Eskin, S. Mozes & N. A. Shah - Unipotent flows and counting lattice points on homogeneous varieties, Ann. of Math. 143 (1996), p. 253-299. | Article | MR 1381987 | Zbl 0852.11054

[29] A. Eskin & H. Oh - Representations of integers by an invariant polynomial and unipotent flows, Duke Math. J. 135 (2006), p. 481-506. | Article | MR 2272974 | Zbl 1138.11011

[30] W. T. Gan & H. Oh - Equidistribution of integer points on a family of homogeneous varieties : a problem of Linnik, Compositio Math. 136 (2003), p. 323-352. | Article | MR 1977010 | Zbl 1018.22009

[31] É. Ghys - Dynamique des flots unipotents sur les espaces homogènes, Séminaire Bourbaki, vol. 1991/92, exposé n° 747, Astérisque 206 (1992), p. 93-136. | EuDML 110165 | Numdam | MR 1206065 | Zbl 0796.58041

[32] A. Gorodnik, F. Maucourant & H. Oh - Manin's and Peyre's conjectures on rational points and adelic mixing, Ann. Sci. Éc. Norm. Super. 41 (2008), p. 383-435. | EuDML 272104 | Numdam | MR 2482443 | Zbl 1161.14015

[33] A. Gorodnik & H. Oh - Rational points on homogeneous varieties and equidistribution of adelic periods, prépublication arXiv:0803. 1996. | MR 2795511

[34] G. Harcos - Equidistribution and L-functions, Lecture Notes Clay Math. School, Pisa 2007.

[35] G. Harcos & P. Michel - The subconvexity problem for Rankin-Selberg L-functions and equidistribution of Heegner points. II, Invent. Math. 163 (2006), p. 581-655. | Article | MR 2207235 | Zbl 1111.11027

[36] B. Host - Nombres normaux, entropie, translations, Israel J. Math. 91 (1995), p. 419-428. | Article | MR 1348326 | Zbl 0839.11030

[37] A. Katok & R. J. Spatzier - Invariant measures for higher-rank hyperbolic abelian actions, Ergodic Theory Dynam. Systems 16 (1996), p. 751-778. | Article | MR 1406432 | Zbl 0859.58021

[38] B. Klingler & A. Yafaev - On the André-Oort conjecture, prépublication, 2006. | Zbl 1377.11073

[39] S. Lang - Algebraic number theory, 2e éd., Graduate Texts in Math., vol. 110, Springer, 1994. | MR 1282723 | Zbl 0811.11001

[40] F. Ledrappier & L.-S. Young - The metric entropy of diffeomorphisms. I and II, Ann. of Math. 122 (1985), p. 509-574. | MR 819557 | Zbl 0605.58028

[41] E. Lindenstrauss - Rigidity of multiparameter actions, Israel J. Math. 149 (2005), p. 199-226. | Article | MR 2191215 | Zbl 1155.37301

[42] E. Lindenstrauss, Invariant measures and arithmetic quantum unique ergodicity, Ann. of Math. 163 (2006), p. 165-219. | Article | MR 2195133 | Zbl 1104.22015

[43] E. Lindenstrauss & B. Weiss - On sets invariant under the action of the diagonal group, Ergodic Theory Dynam. Systems 21 (2001), p. 1481-1500. | Article | MR 1855843 | Zbl 1073.37006

[44] Y. Linnik - Ergodic properties of number fields, Springer, 1970. | MR 238801

[45] G. A. Margulis - Oppenheim conjecture, in Fields Medallists' lectures, World Sci. Ser. 20th Century Math., vol. 5, World Sci. Publ., River Edge, NJ, 1997, p. 272-327. | Article | MR 1622909

[46] G. A. Margulis, Problems and conjectures in rigidity theory, in Mathematics : frontiers and perspectives, Amer. Math. Soc., 2000, p. 161-174. | MR 1754775 | Zbl 0952.22005

[47] G. A. Margulis, On some aspects of the theory of Anosov systems, Springer Monographs in Math., Springer, 2004. | MR 2035655 | Zbl 1140.37010

[48] G. A. Margulis & G. M. Tomanov - Invariant measures for actions of unipotent groups over local fields on homogeneous spaces, Invent. Math. 116 (1994), p. 347-392. | Article | EuDML 144192 | MR 1253197 | Zbl 0816.22004

[49] F. Maucourant - A non-homogeneous orbit closure of a diagonal subgroup, prépublication arXiv:0707.2920, à paraître dans Annals of Math. | MR 2630049 | Zbl 1192.22006

[50] P. Michel & A. Venkatesh - Equidistribution, L-functions and ergodic theory : on some problems of Yu. Linnik, in Proceedings of the International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, p. 421-457. | MR 2275604 | Zbl 1157.11019

[51] P. Michel & A. Venkatesh, Subconvexity for GL 2 , prépublication, 2009.

[52] S. Mozes - Actions of Cartan subgroups, Israel J. Math. 90 (1995), p. 253-294. | Article | MR 1336326 | Zbl 0851.22020

[53] J. Neukirch - Algebraic number theory, Grund. Math. Wiss., vol. 322, Springer, 1999. | MR 1697859 | Zbl 0956.11021

[54] H. Oh - Finiteness of compact maximal flats of bounded volume, Ergodic Theory Dynam. Systems 24 (2004), p. 217-225. | Article | MR 2041269 | Zbl 1048.22002

[55] H. Oh, Orbital counting via mixing and unipotent flows, in Scuola Normale Superiore Summer school, Pisa 2007, Clay Math. Proceedings, vol. 8, 2008. | MR 2648698 | Zbl 1343.11062

[56] V. Platonov & A. Rapinchuk - Algebraic groups and number theory, Pure and Applied Mathematics, vol. 139, Academic Press Inc., 1994. | MR 1278263 | Zbl 0841.20046

[57] A. A. Popa - Central values of Rankin L-series over real quadratic fields, Compos. Math. 142 (2006), p. 811-866. | Article | MR 2249532 | Zbl 1144.11041

[58] M. S. Raghunathan - Discrete subgroups of Lie groups, Ergebnisse Math. Grenzg., vol. 68, Springer, 1972. | MR 507234 | Zbl 0254.22005

[59] M. Ratner - Factors of horocycle flows, Ergodic Theory Dynam. Systems 2 (1982), p. 465-489. | Article | MR 721735 | Zbl 0536.58029

[60] M. Ratner, Rigidity of horocycle flows, Ann. of Math. 115 (1982), p. 597-614. | Article | MR 657240 | Zbl 0506.58030

[61] M. Ratner, Horocycle flows, joinings and rigidity of products, Ann. of Math. 118 (1983), p. 277-313. | Article | MR 717825 | Zbl 0556.28020

[62] M. Ratner, Distribution rigidity for unipotent actions on homogeneous spaces, Bull. Amer. Math. Soc. 24 (1991), p. 321-325. | Article | MR 1069988 | Zbl 0733.22006

[63] M. Ratner, On Raghunathan's measure conjecture, Ann. of Math. 134 (1991), p. 545-607. | Article | MR 1135878 | Zbl 0763.28012

[64] M. Ratner, Raghunathan's topological conjecture and distributions of unipotent flows, Duke Math. J. 63 (1991), p. 235-280. | MR 1106945 | Zbl 0733.22007

[65] D. J. Rudolph - ×2 and ×3 invariant measures and entropy, Ergodic Theory Dynam. Systems 10 (1990), p. 395-406. | Article | MR 1062766 | Zbl 0709.28013

[66] P. C. Sarnak - Diophantine problems and linear groups, in Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), Math. Soc. Japan, 1991, p. 459-471. | MR 1159234 | Zbl 0743.11018

[67] C. Series - On coding geodesics with continued fractions, in Ergodic theory (Sem., Les Plans-sur-Bex, 1980), Monograph. Enseign. Math., vol. 29, Univ. Genève, 1981, p. 67-76. | MR 609896 | Zbl 0476.58018

[68] N. A. Shah - Uniformly distributed orbits of certain flows on homogeneous spaces, Math. Ann. 289 (1991), p. 315-334. | Article | EuDML 164783 | MR 1092178 | Zbl 0702.22014

[69] U. Shapira - A solution to a problem of Cassels and Diophantine properties of cubic fields, prépublication, 2008. | Zbl 1242.11046

[70] G. M. Tomanov - Values of decomposable forms at S-integral points and orbits of tori on homogeneous spaces, Duke Math. J. 138 (2007), p. 533-562. | Article | MR 2322686 | Zbl 1121.22004

[71] G. M. Tomanov & B. Weiss - Closed orbits for actions of maximal tori on homogeneous spaces, Duke Math. J. 119 (2003), p. 367-392. | Article | MR 1997950 | Zbl 1040.22005

[72] E. Ullmo & A. Yafaev - Galois orbits and equidistribution of special subvarieties : towards the André-Oort conjecture, prépublication, 2006.

[73] A. Venkatesh - The work of Einsiedler, Katok and Lindenstrauss on the Littlewood conjecture, Bulletin of the A.M.S. 45 (2008), p. 117-134(électronique). | Article | MR 2358379 | Zbl 1194.11075

[74] A. Venkatesh, Sparse equidistribution problems, period bounds, and subconvexity, pré-publication arXiv:math.NT/0506224. | Article | MR 2680486 | Zbl 1214.11051

[75] J.-L. Waldspurger - Sur les valeurs de certaines fonctions L automorphes en leur centre de symétrie, Compositio Math. 54 (1985), p. 173-242. | EuDML 89702 | Numdam | MR 783511 | Zbl 0567.10021

[76] F. Wlelonsky - Séries d'Eisenstein, intégrales toroïdales et une formule de Hecke, Enseign. Math. 31 (1985), p. 93-135. | MR 798908 | Zbl 0581.12006

[77] S. Zelditch - Selberg trace formulae and equidistribution theorems for closed geodesies and Laplace eigenfunctions : finite area surfaces, Mem. Amer. Math. Soc. 96 (1992). | MR 1101972 | Zbl 0753.11023

[78] S.-W. Zhang - Equidistribution of CM-points on quaternion Shimura varieties, Int. Math. Res. Not. 2005 (2005), p. 3657-3689. | Article | MR 2200081 | Zbl 1096.14016