The residual spectrum of S p 4

Henry H. Kim

Compositio Mathematica (1995)

  • Volume: 99, Issue: 2, page 129-151
  • ISSN: 0010-437X

How to cite


Kim, Henry H.. "The residual spectrum of $Sp_4$." Compositio Mathematica 99.2 (1995): 129-151. <>.

author = {Kim, Henry H.},
journal = {Compositio Mathematica},
keywords = {Eisenstein series; Langlands' method; residual spectrum; Siegel parabolic subgroup},
language = {eng},
number = {2},
pages = {129-151},
publisher = {Kluwer Academic Publishers},
title = {The residual spectrum of $Sp_4$},
url = {},
volume = {99},
year = {1995},

AU - Kim, Henry H.
TI - The residual spectrum of $Sp_4$
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 99
IS - 2
SP - 129
EP - 151
LA - eng
KW - Eisenstein series; Langlands' method; residual spectrum; Siegel parabolic subgroup
UR -
ER -


  1. 1 Arthur, J.: On some problems suggested by the trace formula, in Lie group representations, II, Lecture Notes in Math. 1041Springer-Verlag, 1984, pp. 1-49. Zbl0541.22011MR748504
  2. 2 Borel, A. and Wallach, N.: Continuous cohomology, discrete subgroups, and representations of reductive groups, Annals of Math. Studies94, Princeton University Press, Princeton, 1980. Zbl0443.22010MR554917
  3. 3 Flicker, Y.: On the symmetric square: Applications of a trace formula, Trans. Amer. Math. Soc.330(1) (1992), 125-152. Zbl0761.11027MR1041045
  4. 4 Gelbart, S.: Automorphic forms on Adele groups, Annals of Math. Studies, No 83Princeton University Press, Princeton, 1975. Zbl0329.10018MR379375
  5. 5 Gelbart, S. and Jacquet, H.: A relation between automorphic representations of GL(2) and GL(3), Ann. Sci. Ecole Norm. Sup.11 (1978), 471-542. Zbl0406.10022MR533066
  6. 6 Gelbart, S. and Shahidi, F.: Analytic Properties of Automorphic L-functions, Perspectives in Mathematics, Vol 6, Academic Press, New York, 1988. Zbl0654.10028MR951897
  7. 7 Goldberg, D.: Reducibility of induced representations for Sp(2n) and SO (n), to appear in Amer. J. Math. (1994). Zbl0851.22021MR1296726
  8. 8 Howe, R.: Automorphic forms of low rank, in Non-Commutative Harmonic Analysis, Lecture Notes in Math. 880, Springer-Verlag, 1980, pp. 211-248. Zbl0463.10015MR644835
  9. 9 Ikeda, T.: On the location of poles of the triple L-functions, Comp. Math.83 (1992), 187-237. Zbl0773.11035MR1174424
  10. 10 Jacquet, H.: On the residual spectrum of GL(n), in Lie Group Representations II, Lecture Notes in Math. 1041, Springer-Verlag, 1983, pp. 185-208. Zbl0539.22016MR748508
  11. 11 Jacquet, H. and Langlands, R.P.: Automorphic Forms on GL(2), Lecture Notes in Math. 114, Springer-Verlag, 1970. Zbl0236.12010MR401654
  12. 12 Keys, C.D. and Shahidi, F.: Artin L-functions and normalization of intertwining operators, Ann. Scient. Ec. Norm. Sup.21 (1988), 67-89. Zbl0654.10030MR944102
  13. 13 Kudla, S. and Rallis, S.: Poles of Eisenstein series and L-functions, in Festschrift in Honor of I.I. Piatetski-Shapiro, Part II, Vol. 3, Proc. Israel Mathematical Conf., 1990, pp. 81-110. Zbl0712.11029MR1159110
  14. 14 Kudla, S. and Rallis, S.: On the Weil-Siegel formula, J. Reine Angew. Math.387 (1988), pp. 1-68. Zbl0644.10021MR946349
  15. 15 Kudla, S., Rallis, S., and Soudry, D.: On the degree 5 L-function for Sp(2), Inv. Math.107 (1992), 483-541. Zbl0776.11028MR1150600
  16. 16 Labesse, J.P. and Langlands, R.P.: L-indistinguishability for SL(2), Can. J. Math.31(4) (1979), 726-785. Zbl0421.12014MR540902
  17. 17 Langlands, R.P.: Euler Products, Yale University Press, Yale, 1971. Zbl0231.20016MR419366
  18. 18 Langlands, R.P.: On the Functional Equations Satisfied by Eisenstein Series, Lecture Notes in Math. 544, Springer-Verlag, 1976. Zbl0332.10018MR579181
  19. 19 Moeglin, C.: Orbites unipotentes et spectre discret non ramifie, Le cas des groupes classiques déployś, Comp. Math.77 (1991), 1-54. Zbl0809.11030MR1091891
  20. 20 Moeglin, C. and Waldspurger, J.L.: Décomposition spectrale et séries d'Eisenstein, paraphrase sur l'E-criture, Progress in Mathematics, Birkhäuser, 1994. Zbl0794.11022MR1261867
  21. 21 Piatetski-Shapiro, I. and Rallis, I.: Rankin triple L functions, Comp. Math.64 (1987), 31-115. Zbl0637.10023MR911357
  22. 22 Piatetski-Shapiro, I. and Rallis, I.: A new way to get Euler products, J. Reine Angew. Math.392 (1988), 110-124. Zbl0651.10021MR965059
  23. 23 Schwermer, J.: On Euler Products and Residual Eisenstein Cohomology Classes for Siegel Modular Varieties, Preprint, 1993. Zbl0829.11031MR1307953
  24. 24 Shahidi, F.: On certain L-functions, Amer. J. Math.103 (1981), 297-356. Zbl0467.12013MR610479
  25. 25 Shahidi, F.: A proof of Langlands' conjecture on Plancherel measure; complementary series for p-adic groups, Ann. Math.132 (1990), 273-330. Zbl0780.22005MR1070599
  26. 26 Shahidi, F.: Whittaker models for real groups, Duke Math. J.47(1) (1980), 99-125. Zbl0433.22007MR563369
  27. 27 Shahidi, F.: On the Ramanujan conjecture and finiteness of poles for certain L-functions, Ann. Math.127 (1988), 547-584. Zbl0654.10029MR942520
  28. 28 Shahidi, F.: Langlands' conjecture on Plancherel measures for p-adic groups, in Harmonic Analysis on Reductive Groups, Progress in Math.101, Birkhauser, Boston, 1991, pp. 277-295. Zbl0852.22017MR1168488
  29. 29 Silberger, A.: Introduction to Harmonic Analysis on Reductive p-adic Groups, Math. Notes23, Princeton University Press, Princeton, 1979. Zbl0458.22006MR544991
  30. 30 Soudry, D.: The CAP representations of GSp(4, A), J. Reine Angew. Math.383 (1988), 87-108. Zbl0625.22013MR921988
  31. 31 Watanabe, T.: Residual automorphic representations of Sp 4, Nagoya Math. J.127 (1992), 15-47. Zbl0788.11019MR1183651
  32. 32 Winarsky, N.: Reducibility of principal series representations of p-adic Chevalley groups, Amer. J. Math.100(5) (1978), 941-956. Zbl0475.43005MR517138
  33. 33 Arthur, J.: Eisenstein series and the trace formula, in Proc. Symp. in Pure Mathematics, Part I, Vol. 33, 1979, pp. 253-274. Zbl0431.22016MR546601
  34. 34 Goldstein, L.J.: Analytic Number Theory, Prentice-HallEnglewood Cliffs, NJ, 1971. Zbl0226.12001MR498335
  35. 35 Kim, H. and Shahidi, F.: Quadratic unipotent Arthur parameters and residual spectrum of Sp2n, Preprint. Zbl0866.11036MR1986106
  36. 36 Jantzen, C.: Degenerate principal series for symplectic and odd-orthogonal groups, Preprint, 1994. Zbl0866.22016MR1346929

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.