A relation between automorphic representations of GL ( 2 ) and GL ( 3 )

Stephen Gelbart; Hervé Jacquet

Annales scientifiques de l'École Normale Supérieure (1978)

  • Volume: 11, Issue: 4, page 471-542
  • ISSN: 0012-9593

How to cite

top

Gelbart, Stephen, and Jacquet, Hervé. "A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$." Annales scientifiques de l'École Normale Supérieure 11.4 (1978): 471-542. <http://eudml.org/doc/82024>.

@article{Gelbart1978,
author = {Gelbart, Stephen, Jacquet, Hervé},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {automorphic representations; automorphic forms; GL(2); GL(3); irreducible unitary representation; infinite tensor product; theta-function; Rankin-Selberg method},
language = {eng},
number = {4},
pages = {471-542},
publisher = {Elsevier},
title = {A relation between automorphic representations of $\{\rm GL\}(2)$ and $\{\rm GL\}(3)$},
url = {http://eudml.org/doc/82024},
volume = {11},
year = {1978},
}

TY - JOUR
AU - Gelbart, Stephen
AU - Jacquet, Hervé
TI - A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1978
PB - Elsevier
VL - 11
IS - 4
SP - 471
EP - 542
LA - eng
KW - automorphic representations; automorphic forms; GL(2); GL(3); irreducible unitary representation; infinite tensor product; theta-function; Rankin-Selberg method
UR - http://eudml.org/doc/82024
ER -

References

top
  1. [Bo] A. BOREL, Automorphic L-functions (Proc. of Symposia in Pure Math., Corvallis Conference, Oregon 1977, American Math. Soc., Vol. 33, 1979). Zbl0412.10017
  2. [De] P. DELIGNE, Les constantes des équations fonctionnelles des fonctions L (Springer Lecture Notes, Vol. 349, 1973, pp. 501-598). Zbl0271.14011MR50 #2128
  3. [Ge] S. GELBART, Weil's Representation and the Spectrum of the Metaplectic Group (Springer Lecture Notes, Vol. 530, 1976). Zbl0365.22017MR54 #12654
  4. [Ge Ja] S. GELBART and H. JACQUET, A Relation between Automorphic Forms on GL (2) and GL (3) (Proc. Nat. Acad. Sc. U.S.A., Vol. 73, No. 10, october 1976, pp. 3348-3350). Zbl0373.22008MR54 #283
  5. [Ge J 1] S. GELBART and H. JACQUET, Forms of GL (2) from the Analytic Point of View (Proc. of Symposia in Pure Math., American Math. Soc., Vol. 33, 1979). Zbl0409.22013MR81e:10024
  6. [Go Ja] R. GODEMENT and H. JACQUET, Zeta-functions of Simple Algebras (Springer Lecture Notes, Vol. 260, 1972). Zbl0244.12011MR49 #7241
  7. [Ja] H. JACQUET, Automorphic Forms on GL (2): Part II (Springer Lecture Notes, Vol. 278, 1972). Zbl0243.12005MR58 #27778
  8. [Jl] H. JACQUET, Principal L-functions of the linear group (Proc. of Symposia in Pure Math., American Math. Soc., Vol. 33, 1979). Zbl0413.12007MR81f:22029
  9. [JL] H. JACQUET and R. LANGLANDS, Automorphic Forms on GL (2) (Springer Lecture Notes, Vol. 114, 1970). Zbl0236.12010MR53 #5481
  10. [JPSS] H. JACQUET, I. I. PIATETSKI-SHAPIRO and J. SHALIKA, Automorphic Forms on GL (3) (Annals of Math., Vol. 109, 1979). Zbl0401.10037
  11. [JSh] H. JACQUET and J. SHALIKA, A non-vanishing Theorem for zeta-functions of GLn (Inventiones Math., 38, 1976, pp. 1-16). Zbl0349.12006MR55 #5583
  12. [LL] J.-P. LABESSE and R. P. LANGLANDS, L-indistinguishability for SL (2), Institute for Advanced Study Princeton, 1977, (preprint). 
  13. [La 1] R. P. LANGLANDS, Problems in the Theory of Automorphic Forms (Springer Lecture Notes in Mathematics, Vol. 170, 1970). Zbl0225.14022MR46 #1758
  14. [La 2] R. P. LANGLANDS, On the Functional Equation of the Artin L-Functions, mimeographed notes, Yale University, 1968. 
  15. [La 3] R. P. LANGLANDS, On the Functional Equations satisfied by Eisenstein Series, mimeographed notes, Yale University, 1967. 
  16. [La 4] R. P. LANGLANDS, Base Change for GL (2): The Theory of Saïto-Shintani with Applications, Institute for Advanced Study, Princeton, 1976, (preprint). 
  17. [La 5] R. P. LANGLANDS, On the Notion of an Automorphic Rrepresentation [Proc. of Symposia in Pure Mathematics, Corvallis Conference, Oregon 1977 (to appear)]. Zbl0414.22021
  18. [Ra] R. RANKIN, Contributions to the Theory of Ramanujan's Function τ(n) and Similar Arithmetical Functions (Proc. Camb. Phil. Soc., Vol. 35, 1939, pp. 351-356). Zbl0021.39201MR1,69dJFM65.0353.01
  19. [Si] A. SILBERGER, The Langlands quotient theorem for p-adic groups (preprint). 
  20. [Se] A. SELBERG, On the Estimation of Fourier Coefficients of Modular Forms (Proc. of Symposia in Pure Math., Vol. 8, A.M.S., Providence, R.I., 1965). Zbl0142.33903MR32 #93
  21. [Sh] G. SHIMURA, On the Holomorphy of Certain Dirichlet Series (Proc. London Math. Soc., (3) 31, 1975, pp. 79-95). Zbl0311.10029MR52 #3064
  22. [Ta] J. TATE, Fourier Analysis in Number Fields and Hecke's zeta-function, in Algebraic Number Theory (Proc. of the Brighton Conference, Academic Press, New York, 1968). 
  23. [We 1] A. WEIL, Sur certains groupes d'opérateurs unitaires (Acta Math., Vol. 111, 1964, pp. 143-211). Zbl0203.03305MR29 #2324
  24. [We 2] A. WEIL, On some Exponential Sums (Proc. Nat. Acad. sc., U.S.A., Vol. 34, 1948, pp. 204-207). Zbl0032.26102MR10,234e

Citations in EuDML Documents

top
  1. Amrinder Kaur, Ayyadurai Sankaranarayanan, On certain G L ( 6 ) form and its Rankin-Selberg convolution
  2. J.-L. Waldspurger, Sur les valeurs de certaines fonctions L automorphes en leur centre de symétrie
  3. Nicolas Bergeron, Propriétés de Lefschetz dans la cohomologie de certaines variétés arithmétiques : le cas des surfaces modulaires de Hilbert
  4. Michel Cognet, Représentation de Weil et changement de base quadratique
  5. Tamotsu Ikeda, On the location of poles of the triple L -functions
  6. Freydoon Shahidi, Third symmetric power L -functions for G L ( 2 )
  7. Guy Henniart, Progrès récents en fonctorialité de Langlands
  8. Guangshi Lü, Mean values connected with the Dedekind zeta-function of a non-normal cubic field
  9. Wenzhi Luo, Peter Sarnak, Quantum variance for Hecke eigenforms
  10. Guodong Hua, On higher moments of Hecke eigenvalues attached to cusp forms

NotesEmbed ?

top

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.