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A weak Ramanujan conjecture for generic cuspidal spectrum of quasi-split groups


Author: Freydoon Shahidi
Journal: Bull. Amer. Math. Soc. 15 (1986), 195-200
MSC (1985): Primary 10D40, 12A70, 22E55; Secondary 22E35
DOI: https://doi.org/10.1090/S0273-0979-1986-15470-4
MathSciNet review: 854553
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  • I. N. Bernstein and A. V. Zelevinsky, Induced representations of reductive ${\mathfrak p}$-adic groups. I, Ann. Sci. École Norm. Sup. (4) 10 (1977), no. 4, 441–472. MR 579172
  • A. Borel, Automorphic $L$-functions, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 27–61. MR 546608
  • D. Flath, Decomposition of representations into tensor products, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 179–183. MR 546596
  • Stephen Gelbart and Hervé Jacquet, A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$, Ann. Sci. École Norm. Sup. (4) 11 (1978), no. 4, 471–542. MR 533066
  • R. Howe and I. I. Piatetski-Shapiro, A counterexample to the “generalized Ramanujan conjecture” for (quasi-) split groups, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 315–322. MR 546605
  • Hervé Jacquet, On the residual spectrum of ${\rm GL}(n)$, Lie group representations, II (College Park, Md., 1982/1983) Lecture Notes in Math., vol. 1041, Springer, Berlin, 1984, pp. 185–208. MR 748508, DOI https://doi.org/10.1007/BFb0073148
  • H. Jacquet and J. A. Shalika, On Euler products and the classification of automorphic representations. I, Amer. J. Math. 103 (1981), no. 3, 499–558. MR 618323, DOI https://doi.org/10.2307/2374103
  • Robert P. Langlands, On the functional equations satisfied by Eisenstein series, Lecture Notes in Mathematics, Vol. 544, Springer-Verlag, Berlin-New York, 1976. MR 0579181
  • Robert P. Langlands, Euler products, Yale University Press, New Haven, Conn.-London, 1971. A James K. Whittemore Lecture in Mathematics given at Yale University, 1967; Yale Mathematical Monographs, 1. MR 0419366
  • R. P. Langlands, Problems in the theory of automorphic forms, Lectures in modern analysis and applications, III, Springer, Berlin, 1970, pp. 18–61. Lecture Notes in Math., Vol. 170. MR 0302614
  • R. P. Langlands, Automorphic representations, Shimura varieties, and motives. Ein Märchen, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 205–246. MR 546619
  • 12. C. J. Moreno and F. Shahidi, The L-functions L (s, Symm (r), π), Smith’s Memorial Volume, Canad. Math. Bull. 28 (1985), 405-410.
  • Ichirô Satake, Spherical functions and Ramanujan conjecture, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math.,Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 258–264. MR 0211955
  • Freydoon Shahidi, Functional equation satisfied by certain $L$-functions, Compositio Math. 37 (1978), no. 2, 171–207. MR 498494
  • Freydoon Shahidi, On certain $L$-functions, Amer. J. Math. 103 (1981), no. 2, 297–355. MR 610479, DOI https://doi.org/10.2307/2374219
  • Allan J. Silberger, Introduction to harmonic analysis on reductive $p$-adic groups, Mathematical Notes, vol. 23, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1979. Based on lectures by Harish-Chandra at the Institute for Advanced Study, 1971–1973. MR 544991
  • A. V. Zelevinsky, Induced representations of reductive ${\mathfrak p}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$, Ann. Sci. École Norm. Sup. (4) 13 (1980), no. 2, 165–210. MR 584084

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