Trilinear forms for representations of GL ( 2 ) and local ϵ -factors

Dipendra Prasad

Compositio Mathematica (1990)

  • Volume: 75, Issue: 1, page 1-46
  • ISSN: 0010-437X

How to cite


Prasad, Dipendra. "Trilinear forms for representations of $\mathrm {GL}(2)$ and local $\epsilon $-factors." Compositio Mathematica 75.1 (1990): 1-46. <>.

author = {Prasad, Dipendra},
journal = {Compositio Mathematica},
keywords = {non-archimedean local field; irreducible admissible representations; central characters; Weil-Deligne group; discrete series; G-invariant linear form; supercuspidal},
language = {eng},
number = {1},
pages = {1-46},
publisher = {Kluwer Academic Publishers},
title = {Trilinear forms for representations of $\mathrm \{GL\}(2)$ and local $\epsilon $-factors},
url = {},
volume = {75},
year = {1990},

AU - Prasad, Dipendra
TI - Trilinear forms for representations of $\mathrm {GL}(2)$ and local $\epsilon $-factors
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 75
IS - 1
SP - 1
EP - 46
LA - eng
KW - non-archimedean local field; irreducible admissible representations; central characters; Weil-Deligne group; discrete series; G-invariant linear form; supercuspidal
UR -
ER -


  1. [A-R1] Asmuth, C. and Repka, J.: Tensor product for SL2(k) I, Complementary Series and the Special Representation. Pacific Journal vol. 97, no. 2 (1981). Zbl0445.22015MR641157
  2. [A-R2] Asmuth, C. and Repka, J.: Tensor product for SL2(k) II, Supercuspidal Representations. Pacific Journal vol. 97, no. 1 (1981). Zbl0445.22016MR638168
  3. [Be] Bernstein, J.N.: P-invariant distributions on GL(N) and the classification of unitary representation of GL(N), LNM1041 (1983). Zbl0541.22009
  4. [B-Z] Bernstein, J.N. and Zelevinsky, A.V.: Representations of the group GL(n, F) where F is a nonarchimedean local field. Usp. Mat. Nauk.31, 5-70(1976). Zbl0342.43017MR425030
  5. [Ca] Carayol, H.: Representations cuspidales du groupe linearAnn. Sci. Ecole Norm. Sup.17 (1984) 191-225. Zbl0549.22009MR760676
  6. [Go] Godement: Notes on Jacquet-Langlands theory, IAS, Princeton (1970). Zbl0298.12004
  7. [G-K] Gelfand, I.M. and Kazhdan, D.A.: Representations of GL(n, K), in Lie Groups and Their Representations, Halsted Press1975. 
  8. [G-Ku] Gerardin, P. and Kutzko, P.: Facteurs locaux pour GL(2). Ann. Sci. Ecole Norm. Sup.13 (1980) 349-412. Zbl0448.22015MR597744
  9. [H-K] Harris, M. and Kudla, S.: The central critical value of a triple product L-function, to appear. Zbl0731.11031MR1109355
  10. [Ho] Howe, R.: Kirillov Theory for Compact p-adic Groups. Pacific Journal, vol. 73, no. 2 (1977) 365-381. Zbl0385.22007MR579176
  11. [J-L] Jacquet, H. and Langlands, R.: Automorphic forms on GL2; LNM114 (1970). Zbl0236.12010
  12. [Ko] Koch, H.: Zur Arithmetic in Divisions Algebren Uber Lokalen Korpen, Math. Nachr., 100 (1981) 9-19. Zbl0475.12025MR632618
  13. [Ku 1] Kutzko, P.: On the Supercuspidal representations of GL 2, I, Amer. J. of Math.100 (1978) 43-60. Zbl0417.22012MR507253
  14. [Ku 2] Kutzko, P.: The local Langlands conjecture for GL 2 of a local field, Ann. of Math.112 (1980) 381-412. Zbl0469.22013MR592296
  15. [Ku 3] Kutzko, P.: Formulas For Supercuspidal Representations of GLl, l a prime; American Journal of Math., 109 (1987) 201-222. Zbl0618.22006MR882420
  16. [Ps-R] Piatetski-Shapiro, I. and Rallis, S.: Rankin Triple L-function. Comp. Math.64 (1987) 31-115. Zbl0637.10023MR911357
  17. [Re] Repka, J.: Tensor product of unitary representations of SL2(R); American Journal of Math., 100 (1978). Zbl0402.22010MR509073
  18. [S-S] Sally, P.J. and Shalika, J.A.: Characters of discrete series of representations of SL(2) over a local field, Proc. Nat. Acad. Sci. U.S.A.61 (1968), 1231-1237. Zbl0198.18203MR237713
  19. [Si 1] Silberger, A.: PGL2 over p-adics; LNM166, (1970) 
  20. [Si 2] Silberger, A.: All algebras of spherical functions defined on the two-by-two general linear group with entries in a locally compact p-field are commutative, Proc. Amer. Math. Soc.21 (1969), 437-440. Zbl0174.31205MR237707
  21. [Ta] Tate, J.: Number Theoretic Background, in: Automorphic Forms, Representations, and L-functions (Corvallis), Proc. Symp. Pure Math.33AMS, (1979). Zbl0422.12007MR546607
  22. [Tu] Tunnell, J.: Local ε-factors and characters of GL 2; American J. of Math. vol. 105, no. 6, (1983). Zbl0532.12015
  23. [Wa] Waldspurger, J.-L.: Sur les valeurs de certaines fonctions L automorphes en leur centre de symetrie. Compositio Math.54, 173-242 (1985). Zbl0567.10021MR783511

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.