Theory of spherical functions on reductive algebraic groups over p-adic fields
Publications Mathématiques de l'IHÉS, Tome 18 (1963), p. 5-69
@article{PMIHES_1963__18__5_0,
     author = {Satake, Ichiro},
     title = {Theory of spherical functions on reductive algebraic groups over $p$-adic fields},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {18},
     year = {1963},
     pages = {5-69},
     zbl = {0122.28501},
     mrnumber = {33 \#4059},
     language = {en},
     url = {http://http://www.numdam.org/item/PMIHES_1963__18__5_0}
}
Satake, Ichiro. Theory of spherical functions on reductive algebraic groups over $p$-adic fields. Publications Mathématiques de l'IHÉS, Tome 18 (1963) pp. 5-69. http://www.numdam.org/item/PMIHES_1963__18__5_0/

[1] A. Borel, Groupes linéaires algébriques, Ann. of Math., vol. 64 (1956), pp. 20-82. | MR 19,1195h | Zbl 0070.26104

[2] N. Bourbaki, Éléments de Mathématique, Livre II : Algèbre, chap. 9, " Formes sesquilinéaires et formes quadratiques ", Hermann, Paris, 1959. | MR 86j:13001 | Zbl 0102.25503

[3] F. Bruhat, Distribution sur un groupe localement compact et applications à l'étude des représentations des groupes p-adiques, Bull. Soc. Math. France, vol. 89 (1961), pp. 43-75. | Numdam | MR 25 #4354 | Zbl 0128.35701

[4-5] F. Bruhat, Sur les représentations des groupes classiques p-adiques I, II, Amer. J. Math., vol. 83 (1961), pp. 321-338, 343-368. | MR 23 #A3184 | Zbl 0107.02504

[6] C. Chevalley, L'arithmétique dans les algèbres de matrices, Actualités Sci. et Ind., n° 323, Hermann, Paris, 1936. | JFM 62.0102.01 | Zbl 0014.29006

[7] C. Chevalley, Théorie des groupes de Lie, III, Hermann, Paris, 1955.

[8] J. Dieudonné, La géométrie des groupes classiques, Ergebnisse der Math. und ihre Grenzgebiete, Springer, Berlin, 1955. | MR 17,236a | Zbl 0067.26104

[9] M. Eichler, Quadratische Formen und orthogonale Gruppe, Springer, Berlin-Göttingen-Heidelberg, 1952. | MR 14,540a | Zbl 0049.31106

[10] I. M. Gelfand - M. A. Neumark, Unitäre Darstellungen der klassischen Gruppen, Akademie-Verlag, Berlin, 1957. | Zbl 0077.03405

[11] R. Godement, A theory of spherical functions, I, Trans. Amer. Math. Soc., vol. 73 (1952), pp. 496-556. | MR 14,620c | Zbl 0049.20103

[12] R. Godement, Groupes linéaires algébriques sur un corps parfait, Séminaire Bourbaki, 1960-1961, n° 206. | Numdam | Zbl 0119.27206

[13-14] Harish-Chandra, Spherical functions on a semisimple Lie group, I, II, Amer. J. Math., vol. 80 (1958), pp. 241-310, 553-613. | MR 21 #92 | Zbl 0093.12801

[15] T. Honda, Isogenies, rational points and section points of group varieties, Japanese J. of Math., vol. 30 (1960), pp. 84-101. | MR 27 #5762 | Zbl 0109.39602

[16] S. Lang, Introduction to algebraic geometry, Interscience Publishers, New York, 1958. | MR 20 #7021 | Zbl 0095.15301

[17] F. I. Mautner, Spherical functions over p-adic fields, Amer. J. Math., vol. 80 (1958), pp. 441-457. | MR 20 #82 | Zbl 0092.12501

[18] T. Ono, Arithmetic of algebraic tori, Ann. of Math., vol. 74 (1961), pp. 101-139. | MR 23 #A1640 | Zbl 0119.27801

[19] I. Satake, On spherical functions over p-adic fields, Proc. Japan Acad., vol. 38 (1962), pp. 422-425. | MR 27 #3640 | Zbl 0116.02303

[20] I. Satake, On the theory of reductive algebraic groups over a perfect fields, to appear in J. Math. Soc. Japan, vol. 15 (1963). | MR 27 #1438 | Zbl 0123.25201

[21] G. Shimura, Arithmetic of alternating forms and quaternion hermitian forms, to appear in J. Math. Soc. Japan. | Zbl 0121.28102

[22] T. Tamagawa, On Selberg's trace formula, J. of Fac. of Sci., Univ. of Tokyo, vol. 8 (1960), pp. 363-386. | MR 23 #A958 | Zbl 0118.11405

[23] T. Tamagawa, On the ζ-functions of a division algebra, Ann. of Math., vol. 77 (1963), pp. 387-405. | MR 26 #2468 | Zbl 0222.12018

[24] T. Tsukamoto, On the local theory of quaternionic anti-hermitian forms, J. Math. Soc. Japan, vol. 13 (1961), pp. 387-400. | MR 25 #127 | Zbl 0201.37101

[25] A. Weil, Algebras with involutions and the classical groups, J. Indian Math. Soc., vol. 24 (1960), pp. 589-623. | MR 25 #147 | Zbl 0109.02101

[26] A. Weil, Adèles and algebraic groups, Lectures at the Institute for Advanced Study, Princeton, 1961.