Cogdell, Jim W.; Piatetski-Shapiro, I. I.
Converse theorems for GL n
Publications Mathématiques de l'IHÉS, Tome 79 (1994) , p. 157-214
Zbl 0814.11033 | MR 95m:22009 | 7 citations dans Numdam
URL stable : http://www.numdam.org/item?id=PMIHES_1994__79__157_0

Bibliographie

[1] H. Bass, K-theory and stable algebra, Publ. Math. IHES, 22 (1964), 5-60. Numdam | MR 30 #4805 | Zbl 0248.18025

[2] H. Bass, J. Milnor, and J.-P. Serre, Solution of the congruence subgroup problem for SLn(n ≥ 3) and Sp2n (n ≥ 2), Publ. Math. IHES, 33 (1967), 59-137. Numdam | MR 39 #5574 | Zbl 0174.05203

[3] J. N. Bernstein and A. V. Zelevinsky, Representations of the group GL(n, F) where F is a non-archimedean local field, Russian Math. Surveys, 31:3 (1976), 1-68. Zbl 0348.43007

[4] J. N. Bernstein and A. V. Zelevinsky, Induced representations of reductive p-adic groups, I, Ann. scient. Ec. Norm. Sup., 4e série, 10 (1977), 441-472. Numdam | MR 58 #28310 | Zbl 0412.22015

[5] A. Borel, Automorphic L-functions, Proc. Symp. Pure Math., 33, part 2 (1979), 27-61. MR 81m:10056 | Zbl 0412.10017

[6] A. Borel and H. Jacquet, Automorphic forms and representations, Proc. Symp. Pure Math., 33, part 1 (1979), 189-202. MR 81m:10055 | Zbl 0414.22020

[7] A. Borel and N. Wallach, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive groups, Annals of Mathematics Study, No. 94, Princeton, Princeton University Press, 1980. MR 83c:22018 | Zbl 0443.22010

[8] P. Cartier, Representations of p-adic groups : a survey, Proc. Symp. Pure math., 33, part 1 (1979), 111-155. MR 81e:22029 | Zbl 0421.22010

[9] W. Casselman, Introduction to the theory of admissible representations of p-adic reductive groups, manuscript, 1975,

[10] W. Casselman, Canonical extensions of Harish Chandra modules, Can. J. Math., XLI (1989), 385-438. MR 90j:22013 | Zbl 0702.22016

[11] L. Clozel, Représentations galoisiennes associées aux représentations automorphes autoduales de GL(n), Publ. Math. IHES, 73 (1991), 97-145. Numdam | MR 92i:11055 | Zbl 0739.11020

[12] D. Flath, Decomposition of representations into tensor products, Proc. Symp. Pure Math., 33, part 1 (1979), 179-183. MR 81f:22028 | Zbl 0414.22019

[13] I. M. Gelfand, M. I. Graev and I. I. Piatetski-Shapiro, Representation Theory and Automorphic Functions, Boston, Academic Press, 1990. MR 91g:11052 | Zbl 0718.11022

[14] R. Godement, Introduction à la théorie de Langlands, Séminaire Bourbaki, 1966-1967, N°. 321. Numdam | Zbl 0216.15001

[15] H. Hamburger, Über die Riemannsche Funktionalgleichung der ζ-Funktion, Math. Zeit., 10 (1921), 240-254 ; 11 (1922), 224-245 ; 13 (1922), 283-311. JFM 48.1210.03

[16] G. Harder, Minkowskische Reductionstheorie über Funktionenköpern, Inv. Math., 7 (1969), 33-54. MR 44 #1667 | Zbl 0242.20046

[17] E. Hecke, Über die Bestimung Dirichletscher Reihen durch ihre Funktionalgleichung, Math. Ann., 112 (1936), 664-699. JFM 62.1207.01 | Zbl 0014.01601

[18] E. Hecke, Mathematische Werke, Göttingen, Vandenhoeck und Ruprecht, 1959. MR 21 #3303 | Zbl 0092.00102

[19] H. Jacquet, Generic representations, in Non-commutative Harmonic Analysis, Lecture Notes in Mathematics No. 587, Berlin-Heidelberg-New York, Springer Verlag, 1977, p. 91-101. MR 58 #16985 | Zbl 0357.22010

[20] H. Jacquet, Principal L-functions of the linear group, Proc. Symp. Pure Math., 33, part 1 (1979), 111-155. MR 81f:22029 | Zbl 0413.12007

[21] H. Jacquet and R. P. Langlands, Automorphic Forms on GL(2), Lecture Notes in Mathematics No. 114, Berlin-Heidelberg-New York, Springer Verlag, 1970. MR 53 #5481 | Zbl 0236.12010

[22] H. Jacquet, I. I. Piatetski-Shapiro and J. Shalika, Automorphic forms on GL(3), I & II, Ann. of Math., 109 (1979), 169-258. MR 80i:10034a | Zbl 0401.10037

[23] H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika, Conducteur des représentations du groupe linéaire, Math. Ann., 256 (1981), 199-214. MR 83c:22025 | Zbl 0443.22013

[24] H. Jacquet, I. I. Piatetski-Shapiro and J. Shalika, Rankin-Selberg Convolutions, Am. J. Math., 105 (1983), 367-464. MR 85g:11044 | Zbl 0525.22018

[25] H. Jacquet and J. Shalika, On Euler products and the classification of automorphic representations, I, Am. J. Math., 103 (1981), 449-558 ; II, 103 (1981), 777-815. Zbl 0491.10020

[26] H. Jacquet and J. Shalika, The Whittaker models of induced representations, Pacific J. Math., 109 (1983), 107-120. MR 85h:22023 | Zbl 0535.22017

[27] H. Jacquet and J. Shalika, Rankin-Selberg Convolutions : Archimedean Theory, Festschrift in Honor of I. I. Piatetski-Shapiro, part I, Rehovot, Weizmann Science Press, 1990, p. 125-207. MR 93d:22022 | Zbl 0712.22011

[28] N. Jacobson, Basic Algebra II, San Francisco, W. H. Freeman and Co., 1980. MR 81g:00001 | Zbl 0441.16001

[29] A. Knapp, Local Langlands correspondence : Archimedean case, Proc. Symp. Pure Math., 55, part 2 (1994), 393-410. MR 95d:11066 | Zbl 0811.11071

[30] M. Kneser, Strong approximation, Proc. Symp. Pure Math., 9 (1966), 187-196. MR 35 #4225 | Zbl 0201.37904

[31] B. Kostant, On Whittaker vectors and representation theory, Inv. Math., 48 (1978), 101-184. MR 80b:22020 | Zbl 0405.22013

[32] J.-P. Labesse and J. Schwermer, On liftings and cusp cohomology of arithmetic groups, Inv. Math., 83 (1986), 383-401. MR 87g:11060 | Zbl 0581.10013

[33] R. P. Langlands, On the Functional Equation Satisfied by Eisenstein Series, Lecture Notes in Mathematics No. 544, New York, Springer Verlag, 1976. MR 58 #28319 | Zbl 0332.10018

[34] R. P. Langlands, On the notion of an automorphic representation, Proc. Symp. Pure Math., 33, part 1 (1979), 203-207. Zbl 0414.22021

[35] H. Maass, Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann., 121 (1944), 141-183. MR 11,163c | Zbl 0033.11702

[36] C. Moeglin and J.-L. Waldspurger, Décomposition spectrale et Séries d'Einstein. Une paraphrase de l'écriture, Boston, Birkhäuser, 1994. Zbl 0794.11022

[37] O. T. O'Meara, Introduction to Quadratic Forms, Berlin-Göttingen-Heidelberg, Springer Verlag, 1963. MR 27 #2485 | Zbl 0107.03301

[38] I. I. Piatetski-Shapiro, Zeta-functions of GL(n), Preprint, University of Maryland, 1976.

[39] I. I. Piatetski-Shapiro, The converse theorem for GL(n), Festschrift in Honor of I. I. Piatetski-Shapiro, part II, Rehovot, Weizmann Science Press, 1990, p. 185-195. MR 93b:11062 | Zbl 0708.11031

[40] F. Rodier, Whittaker models for admissible representations of reductive p-adic split groups, Proc. Symp. Pure Math., 26 (1973), 425-430. MR 50 #7419 | Zbl 0287.22016

[41] G. Shimura, On Dirichlet series and Abelian varieties attached to automorphic forms, Ann. Math., 76 (1962), 237-294. MR 33 #1292 | Zbl 0142.05501

[42] A. Weil, Über die Bestimung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann., 168 (1967), 149-156. MR 34 #7473 | Zbl 0158.08601