Changement du corps de base pour les représentations de G L ( 2 )

Paul Gérardin

Séminaire Bourbaki (1977-1978)

  • Volume: 20, page 65-88
  • ISSN: 0303-1179

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Gérardin, Paul. "Changement du corps de base pour les représentations de $GL(2)$." Séminaire Bourbaki 20 (1977-1978): 65-88. <http://eudml.org/doc/109928>.

@article{Gérardin1977-1978,
author = {Gérardin, Paul},
journal = {Séminaire Bourbaki},
keywords = {Gl(2)-Theory; Langlands Conjecture; Local Field; Adeles of Algebraic Numbers},
language = {fre},
pages = {65-88},
publisher = {Springer-Verlag},
title = {Changement du corps de base pour les représentations de $GL(2)$},
url = {http://eudml.org/doc/109928},
volume = {20},
year = {1977-1978},
}

TY - JOUR
AU - Gérardin, Paul
TI - Changement du corps de base pour les représentations de $GL(2)$
JO - Séminaire Bourbaki
PY - 1977-1978
PB - Springer-Verlag
VL - 20
SP - 65
EP - 88
LA - fre
KW - Gl(2)-Theory; Langlands Conjecture; Local Field; Adeles of Algebraic Numbers
UR - http://eudml.org/doc/109928
ER -

References

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  1. [1] R.P. Langlands - Base change for GL(2) , the theory of Saito-Shintani with applications, Notes, I.A.S., Princeton, 1975. 
  2. [2] Automorphic forms, Representations, and L-functions, A.M.S. Summer Institute 1977, Corvallis, à paraître. 
  3. [contient notamment : Automorphic L-functions ( A.. Borel), 
  4. Number theoretic back-ground ( J. Tate), 
  5. Decomposition of representations into tensor products ( D. Flath), 
  6. General properties of representations ( P. Cartier), 
  7. Forms on GL(2) from the analytic point of view ( S. Gelbart- H. Jacquet), 
  8. Base change for GL(2) ( R. Kottwitz, P. Gérardin, J.-P. Labesse).] Zbl0412.10018
  9. [3] K. Doi, H. Naganuma - On the algebraic curves uniformized by arithmetical automorphic functions, Ann. of Math., 86 (1967), 449-460. Zbl0217.05002MR219537
  10. [4] K. Doi, H. Naganuma - On the functional equation of certain Dirichletseries, Inventiones Math., 9 (1964), 1-14. Zbl0182.54301MR253990
  11. [5] G. Shimura - Arithmetic theory of automorphic functions, Iwanami Shoten Pub. and Princeton Univ. Press, 1971. Zbl0221.10029MR314766
  12. Voir aussi les articles de M. Cohen, S. Kudla, et D. Zagier dans 
  13. [6] Modular functions of one variable V , VI, à paraître aux Lecture Notes in Math., (vol. 601 et ? ), Springer-Verlag. 
  14. [7] H. Saito - Automorphic forms and algebraic extensions of number fields, L. N. n° 8, Tokyo, 1975. Zbl0381.10025MR384703
  15. [8] T. Shintani - On liftings of holomorphic automorphic forms, U.S.-Japan Seminar on number Theory, Ann Arbor, Mich., 1975. 
  16. [9] T. Shintani - Two remarks on irreducible characters of finite general linear groups, J. Math. Soc. Jap., 28 (1976), 396-414. Zbl0323.20041MR414730
  17. [10] H. Jacquet, R.P. Langlands - Automorphic forms on GL(2) , Lecture Notes in Math., vol. 114, Springer-Verlag, 1970. Zbl0236.12010MR401654
  18. [11] A. Robert - Formes automorphes sur GL(2) (Travaux de H. Jacquet et R. P. Langlands), Sém. Bourbaki, exposé 415, Lecture Notes in Math., vol. 317, Springer-Verlag, 1973. Zbl0254.10022MR424697
  19. [12] S. Gelbart - Automorphic forms on adèle groups, Ann. of Math. St. 83, Princeton Univ. Press, 1975. Zbl0329.10018MR379375
  20. [13] Modular functions of one variable II, Lecture Notes in Math., vol. 349, Springer-Verlag, 1973. 
  21. [14] R.P. Langlands - Problems in the theory of automorphics forms, in Lecture Notes in Math., vol. 170, Springer-Verlag, 18-86, 1970. Zbl0225.14022MR302614
  22. [15] A. Borel - Formes automorphes et séries de Dirichlet (d'après R.P. Langlands), Lecture Notes in Math., Sém. Bourbaki, exposé 466, vol. 567, Springer-Verlag, 1977. Zbl0329.10019MR447118
  23. [16] S. Gelbart, H. Jacquet - A relation between automorphic forms on GL(2) and GL(3), Proc. Nat. Acad. Sci. U.S.A., 1976, 3348-3350. Zbl0373.22008MR412156
  24. [17] H. Jacquet - Automorphic forms on GL(2) , II, Lecture Notes in Math., vol.278, Springer-Verlag, 1972. Zbl0243.12005MR562503
  25. [18] H. Jacquet, I.I. Piatetskii-Shapiro, J. Shalika - Construction of cusp-forms for GL(3) , L.N. n° 16, Univ. of Maryland, 1975. MR498394
  26. [19] H. Jacquet, J. Shalika - Comparaison des formes automorphes du groupe linéaire, C.R.Acad. Sci. Paris, 284 (1977), 741-744. Zbl0372.22012MR432551
  27. [20] J.-P. Labesse, R.P. Langlands - L-indistinguishability for SL(2) , Preprint I.A.S., Princeton, 1977. MR540902
  28. [21] W. Casselman - On somes results of Atkin and Lehner, Math. Ann., 201(1973),301-334. Zbl0239.10015MR337789
  29. [22] J. Cassels, A. Frohlich - Algebraic number theory, Acad. Press., 1967. Zbl0153.07403MR215665
  30. [23] R. Godement, H. Jacquet - Zeta functions a simple algebras, Lecture Notes in Math., vol. 260, Springer-Verlag,1970. Zbl0244.12011
  31. [24] I. Satake - Theory of spherical functions on reductive algebraic groups over p-adic fields, Pub. Math. I.H.E.S., 18(1963), 5-69. Zbl0122.28501MR195863
  32. [25] J.-P. Serre - Représentations linéaires des groupes finis, Hermann, Paris, 1967. Zbl0407.20003MR232867

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