@article{PMIHES_1994__79__157_0, author = {Cogdell, Jim W. and Piatetski-Shapiro, I. I.}, title = {Converse theorems for $GL_n$}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {157--214}, publisher = {Institut des Hautes \'Etudes Scientifiques}, volume = {79}, year = {1994}, mrnumber = {1307299}, zbl = {0814.11033}, language = {en}, url = {http://archive.numdam.org/item/PMIHES_1994__79__157_0/} }
TY - JOUR AU - Cogdell, Jim W. AU - Piatetski-Shapiro, I. I. TI - Converse theorems for $GL_n$ JO - Publications Mathématiques de l'IHÉS PY - 1994 SP - 157 EP - 214 VL - 79 PB - Institut des Hautes Études Scientifiques UR - http://archive.numdam.org/item/PMIHES_1994__79__157_0/ LA - en ID - PMIHES_1994__79__157_0 ER -
Cogdell, Jim W.; Piatetski-Shapiro, I. I. Converse theorems for $GL_n$. Publications Mathématiques de l'IHÉS, Tome 79 (1994), pp. 157-214. http://archive.numdam.org/item/PMIHES_1994__79__157_0/
[1] K-theory and stable algebra, Publ. Math. IHES, 22 (1964), 5-60. | Numdam | MR | Zbl
,[2] Solution of the congruence subgroup problem for SLn(n ≥ 3) and Sp2n (n ≥ 2), Publ. Math. IHES, 33 (1967), 59-137. | Numdam | MR | Zbl
, , and ,[3] Representations of the group GL(n, F) where F is a non-archimedean local field, Russian Math. Surveys, 31:3 (1976), 1-68. | Zbl
and ,[4] Induced representations of reductive p-adic groups, I, Ann. scient. Ec. Norm. Sup., 4e série, 10 (1977), 441-472. | Numdam | MR | Zbl
and ,[5] Automorphic L-functions, Proc. Symp. Pure Math., 33, part 2 (1979), 27-61. | MR | Zbl
,[6] Automorphic forms and representations, Proc. Symp. Pure Math., 33, part 1 (1979), 189-202. | MR | Zbl
and ,[7] Continuous Cohomology, Discrete Subgroups, and Representations of Reductive groups, Annals of Mathematics Study, No. 94, Princeton, Princeton University Press, 1980. | MR | Zbl
and ,[8] Representations of p-adic groups : a survey, Proc. Symp. Pure math., 33, part 1 (1979), 111-155. | MR | Zbl
,[9] Introduction to the theory of admissible representations of p-adic reductive groups, manuscript, 1975,
,[10] Canonical extensions of Harish Chandra modules, Can. J. Math., XLI (1989), 385-438. | MR | Zbl
,[11] Représentations galoisiennes associées aux représentations automorphes autoduales de GL(n), Publ. Math. IHES, 73 (1991), 97-145. | Numdam | MR | Zbl
,[12] Decomposition of representations into tensor products, Proc. Symp. Pure Math., 33, part 1 (1979), 179-183. | MR | Zbl
,[13] Representation Theory and Automorphic Functions, Boston, Academic Press, 1990. | MR | Zbl
, and ,[14] Introduction à la théorie de Langlands, Séminaire Bourbaki, 1966-1967, N°. 321. | Numdam | Zbl
,[15] Über die Riemannsche Funktionalgleichung der ζ-Funktion, Math. Zeit., 10 (1921), 240-254 ; 11 (1922), 224-245 ; 13 (1922), 283-311. | JFM
,[16] Minkowskische Reductionstheorie über Funktionenköpern, Inv. Math., 7 (1969), 33-54. | MR | Zbl
,[17] Über die Bestimung Dirichletscher Reihen durch ihre Funktionalgleichung, Math. Ann., 112 (1936), 664-699. | JFM | Zbl
,[18] Mathematische Werke, Göttingen, Vandenhoeck und Ruprecht, 1959. | MR | Zbl
,[19] Generic representations, in Non-commutative Harmonic Analysis, Lecture Notes in Mathematics No. 587, Berlin-Heidelberg-New York, Springer Verlag, 1977, p. 91-101. | MR | Zbl
,[20] Principal L-functions of the linear group, Proc. Symp. Pure Math., 33, part 1 (1979), 111-155. | MR | Zbl
,[21] Automorphic Forms on GL(2), Lecture Notes in Mathematics No. 114, Berlin-Heidelberg-New York, Springer Verlag, 1970. | MR | Zbl
and ,[22] Automorphic forms on GL(3), I & II, Ann. of Math., 109 (1979), 169-258. | MR | Zbl
, and ,[23] Conducteur des représentations du groupe linéaire, Math. Ann., 256 (1981), 199-214. | MR | Zbl
, , and ,[24] Rankin-Selberg Convolutions, Am. J. Math., 105 (1983), 367-464. | MR | Zbl
, and ,[25] On Euler products and the classification of automorphic representations, I, Am. J. Math., 103 (1981), 449-558 ; II, 103 (1981), 777-815. | Zbl
and ,[26] The Whittaker models of induced representations, Pacific J. Math., 109 (1983), 107-120. | MR | Zbl
and ,[27] Rankin-Selberg Convolutions : Archimedean Theory, Festschrift in Honor of I. I. Piatetski-Shapiro, part I, Rehovot, Weizmann Science Press, 1990, p. 125-207. | MR | Zbl
and ,[28] Basic Algebra II, San Francisco, W. H. Freeman and Co., 1980. | MR | Zbl
,[29] Local Langlands correspondence : Archimedean case, Proc. Symp. Pure Math., 55, part 2 (1994), 393-410. | MR | Zbl
,[30] Strong approximation, Proc. Symp. Pure Math., 9 (1966), 187-196. | MR | Zbl
,[31] On Whittaker vectors and representation theory, Inv. Math., 48 (1978), 101-184. | MR | Zbl
,[32] On liftings and cusp cohomology of arithmetic groups, Inv. Math., 83 (1986), 383-401. | MR | Zbl
and ,[33] On the Functional Equation Satisfied by Eisenstein Series, Lecture Notes in Mathematics No. 544, New York, Springer Verlag, 1976. | MR | Zbl
,[34] On the notion of an automorphic representation, Proc. Symp. Pure Math., 33, part 1 (1979), 203-207. | Zbl
,[35] Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann., 121 (1944), 141-183. | MR | Zbl
,[36] Décomposition spectrale et Séries d'Einstein. Une paraphrase de l'écriture, Boston, Birkhäuser, 1994. | Zbl
and ,[37] Introduction to Quadratic Forms, Berlin-Göttingen-Heidelberg, Springer Verlag, 1963. | MR | Zbl
,[38] Zeta-functions of GL(n), Preprint, University of Maryland, 1976.
,[39] 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 | Zbl
,[40] Whittaker models for admissible representations of reductive p-adic split groups, Proc. Symp. Pure Math., 26 (1973), 425-430. | MR | Zbl
,[41] On Dirichlet series and Abelian varieties attached to automorphic forms, Ann. Math., 76 (1962), 237-294. | MR | Zbl
,[42] Über die Bestimung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann., 168 (1967), 149-156. | MR | Zbl
,