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References

  1. J. Arthur, The principle of functoriality, Bull. Am. Math. Soc., 40 (2002), 39–53.

    Google Scholar 

  2. A. Borel, Automorphic L-functions, Proc. Symp. Pure Math., 33, part 2 (1979), 27–61.

    Google Scholar 

  3. N. Bourbaki, Algèbre Commutative, Ch. 3 et 4, Actualités Scientifiques et Industrielles, no. 1293. Hermann, Paris (1961).

  4. W. Casselman and F. Shahidi, On reducibility of standard modules for generic representations, Ann. Sci. Éc. Norm. Supér., 31 (1998), 561–589.

    Google Scholar 

  5. J. W. Cogdell, Dual groups and Langlands Functoriality, An Introduction to the Langlands Program (J. Bernstein and S. Gelbart, eds.). Birkhäuser, Boston (2003), 251–268.

  6. J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, On lifting from classical groups to GLN, Publ. Math., Inst. Hautes Étud. Sci., 93 (2001), 5–30.

    Google Scholar 

  7. J. W. Cogdell and I. I. Piatetski-Shapiro, Converse Theorems for GL n , Publ. Math., Inst. Hautes Étud. Sci., 79 (1994), 157–214.

  8. J. W. Cogdell and I. I. Piatetski-Shapiro, Stability of gamma factors for SO(2n+1), Manuscr. Math., 95 (1998), 437–461.

    Google Scholar 

  9. J. W. Cogdell and I. I. Piatetski-Shapiro, Converse Theorems for GL n , II, J. Reine Angew. Math., 507 (1999), 165–188.

    Google Scholar 

  10. J. W. Cogdell, I. I. Piatetski-Shapiro, and F. Shahidi, On stability of local γ-factors, in preparation.

  11. S. Gelbart and H. Jacquet, A relation between automorphic representations of GL(2) and GL(3), Ann. Sci. Éc. Norm. Supér., IV. Sér.,11 (1978), 471–542.

    Google Scholar 

  12. S. Gelbart and F. Shahidi, Boundedness of automorphic L-functions in vertical strips, J. Am. Math. Soc., 14 (2001), 79–107.

    Google Scholar 

  13. D. Ginzburg, S. Rallis, and D. Soudry, Generic automorphic forms on SO(2n+1): functorial lift to GL(2n), endoscopy, and base change, Int. Math. Res. Not., 2001, no. 14 (2001), 729–764.

  14. R. Godement and H. Jacquet, Zeta Functions of Simple Algebras, Lect. Notes Math., 260. Springer-Verlag, Berlin (1972).

  15. M. Harris and R. Taylor, The Geometry and Cohomology of Some Simple Shimura Varieties, Ann. Math. Stud., 151. Princeton University Press, Princeton (2001).

  16. G. Henniart, Caractérisation de la correspondance de Langlands locale par les facteurs ε de paires, Invent. Math., 113 (1993), 339–350.

    Google Scholar 

  17. G. Henniart, Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique, Invent. Math., 139 (2000), 439–455.

    Google Scholar 

  18. R. Howe and I. I. Piatetski-Shapiro, A counter-example to the “generalized Ramanujan conjecture” for (quasi)-split groups, Proc. Symp. Pure Math., 33, part 1 (1979), 315–322.

    Google Scholar 

  19. H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika, Conducteur des représentations du groupe linéaire., Math. Ann., 256 (1981), 199–214.

    Google Scholar 

  20. H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika, Rankin-Selberg convolutions, Am. J. Math., 105 (1983), 367–464.

    Google Scholar 

  21. H. Jacquet and J. Shalika, On Euler products and the classification of automorphic representations, Am. J. Math., 103 (1981), 499–558 and 777–815.

    Google Scholar 

  22. H. Jacquet and J. Shalika, The Whittaker models for induced representations, Pac. J. Math., 109 (1983), 107–120.

    Google Scholar 

  23. H. Jacquet and J. Shalika, A lemma on highly ramified ε-factors, Math. Ann., 271 (1985), 319–332.

    Google Scholar 

  24. C. Jantzen, On square integrable representations of classical p-adic groups, Can. J. Math., 52 (2000), 539–581.

    Google Scholar 

  25. C. Jantzen, On square integrable representations of classical p-adic groups II, Represent. Theory, 4 (2000), 127–180.

    Google Scholar 

  26. D. Jiang and D. Soudry, The local converse theorem for SO(2n+1) and applications, Ann. Math., 157 (2003), 743–806.

    Google Scholar 

  27. D. Jiang and D. Soudry, Generic representations and local Langlands reciprocity law for p-adic SO2n+1, Contributions to Automorphic Forms, Geometry and Number Theory (Shalikafest 2002) (H. Hida, D. Ramakrishnan, and F. Shahidi, eds.). Johns Hopkins University Press, Baltimore, to appear.

  28. H. Kim, Langlands–Shahidi method and poles of automorphic L-functions, II, Isr. J. Math., 117 (2000), 261–284.

    Google Scholar 

  29. H. Kim, Residual spectrum of odd orthogonal groups, Int. Math. Res. Not.2001, no. 17 (2001), 873–906.

  30. H. Kim, Applications of Langlands’ functoriality of odd orthogonal groups, Trans. Am. Math. Soc., 354 (2002), 2775–2796.

    Google Scholar 

  31. H. Kim, On local L-functions and normalized intertwining operators, Can. J. Math., to appear.

  32. H. Kim and F. Shahidi, Functorial products for GL2×GL3 and the symmetric cube for GL2, Ann. Math., 155 (2002), 837–893.

    Google Scholar 

  33. L. Lafforgue, Chtoucas de Drinfeld at correspondance de Langlands, Invent. Math., 147 (2002) 1–241.

  34. R. P. Langlands, On the classification of irreducible representations of real algebraic groups, Representation Theory and Harmonic Analysis on Semisimple Lie Groups, Math. Surv. Monogr., 31. Am. Math. Soc., Providence, RI (1989), 101–170.

  35. R. P. Langlands, Automorphic representations, Shimura varieties, and motives. Ein Märchen, Proc. Symp. Pure Math., 33, part 2 (1979), 205–246.

  36. R. P. Langlands, Where stands functoriality today, Proc. Symp. Pure Math., 61 (1997), 457–471.

    Google Scholar 

  37. W. Luo, Z. Rudnick, and P. Sarnak, On the generalized Ramanujan conjecture for GL(n), Proc. Symp. Pure Math., 66, part 2 (1999), 301–310.

  38. C. Moeglin, Points de réducibilité pour les induits de cuspidals, preprint (2001).

  39. C. Moeglin, Sur la classification des séries discrètes des groupes classiques p-adiques: paramètres de Langlands et exhaustivité, J. Eur. Math. Soc., 4 (2002), 141–200.

    Google Scholar 

  40. C. Moeglin and M. Tadić, Construction of discrete series for p-adic classical groups, J. Am. Math. Soc., 15 (2002), 715–786.

    Google Scholar 

  41. C. Moeglin and J-L. Waldspurger, Le spectre résiduel de GL(n), Ann. Sci. Éc. Norm. Supér., 22 (1989), 605–674.

    Google Scholar 

  42. G. Muić, On generic irreducible representations of Sp(n,F) and SO(2n+1,F), Glas. Mat., III. Ser., 33 (53) (1998), 19–31.

    Google Scholar 

  43. G. Muić, Some results on square integrable representations; Irreducibility of standard representations, Int. Math. Res. Not., 1998, no. 14 (1998), 705–726.

  44. G. Muić, A proof of Casselman-Shahidi’s conjecture for quasi-split classical groups, Can. Math. Bull., 44 (2001), 298–312.

    Google Scholar 

  45. I. I. Piatetski-Shapiro, Multiplicity one theorems, Proc. Symp. Pure Math., 33, part 1 (1979), 209–212.

  46. P. Sarnak, Estimates for Rankin-Selberg L-functions and quantum unique ergodicity, J. Funct. Anal., 184 (2001), 419–453.

    Google Scholar 

  47. I. Satake, Theory of spherical functions on reductive algebraic groups over \(\mathfrak{p}\)-adic fields, Publ. Math., Inst. Hautes Étud. Sci., 18 (1963), 5–69.

  48. F. Shahidi, On certain L-functions, Am. J. Math., 103 (1981), 297–355.

    Google Scholar 

  49. F. Shahidi, Local coefficients as Artin factors for real groups, Duke Math. J., 52 (1985), 973–1007.

  50. F. Shahidi, On the Ramanujan conjecture and finiteness of poles for certain L-functions, Ann. Math., 127 (1988), 547–584.

    Google Scholar 

  51. F. Shahidi, A proof of Langlands’ conjecture on Plancherel measures; complementary series for p-adic groups, Ann. Math., 132 (1990), 273–330.

    Google Scholar 

  52. F. Shahidi, On multiplicativity of local factors, Festschrift in honor of I. I. Piatetski-Shapiro on the occasion of his sixtieth birthday, part II (Ramat Aviv, 1989), Israel Math. Conf. Proc., 3, Weizmann, Jerusalem (1990), 279–289.

  53. F. Shahidi, Twisted endoscopy and reducibility of induced representations for p-adic groups, Duke Math. J., 66 (1992), 1–41.

    Google Scholar 

  54. F. Shahidi, Twists of a general class of L-functions by highly ramified characters, Can. Math. Bull., 43 (2000), 380–384.

    Google Scholar 

  55. F. Shahidi, Local coefficients as Mellin transforms of Bessel functions; Towards a general stability, Int. Math. Res. Not., 2002, no. 39 (2002), 2075–2119.

  56. D. Soudry, On Langlands functoriality from classical groups to GL n , Astérisque, to appear.

  57. R. Steinberg, Lectures on Chevalley Groups. Yale Lecture Notes, New Haven (1967).

  58. M. Tadić, Classification of unitary representations in irreducible representations of general linear groups (non-Archimedean case), Ann. Sci. Éc. Norm. Supér., IV. Sér., 19 (1986), 335–382.

  59. J. Tate, Number theoretic background, Proc. Symp. Pure Math., 33, part 2 (1979), 3–26.

    Google Scholar 

  60. D. Vogan, Gelfand-Kirillov dimension for Harish-Chandra modules, Invent. Math., 48 (1978), 75–98.

    Google Scholar 

  61. A. Zelevinsky, Induced representations of reductive \(\mathfrak{p}\)–adic groups, II, Ann. Sci. Éc. Norm. Supér., 13 (1980), 165–210.

    Google Scholar 

  62. Y. Zhang, The holomorphy and nonvanishing of normalized local intertwining operators, Pac. J. Math., 180 (1997), 386–398.

    Google Scholar 

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Cogdell, J., Kim, H., Piatetski-Shapiro, I. et al. Functoriality for the classical groups. Publ. Math., Inst. Hautes Étud. Sci. 99, 163–233 (2004). https://doi.org/10.1007/s10240-004-0020-z

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