Abstract
We show that for the quasi-split unitary group in three variables every tempered packet of cuspidal automorphic representations contains a globally generic representation.
Similar content being viewed by others
References
J. Arthur,A trace formula for reductive groups I: Terms associated to classes in G(ℚ), Duke Mathematical Journal45 (1978), 912–952.
J. Arthur,A trace formula for reductive groups II: Applications of a truncation operator, Compositio Mathematica40 (1980), 87–121.
J. Arthur,The trace formula in invariant form, Annals of Mathematics114 (1981), 1–74.
T. Asai,On Certain Dirichlet series associated with Hilbert modular forms, Mathematische Annalen226 (1977), 81–94.
E. M. Baruch,Proof of Kirillov’s conjecture, preprint.
E. M. Baruch and Z. Mao,Central critical value of automorphic L-functions, preprint
J. Bernstein,P-invariant distributions of GL(n) and the classification of unitary representations of GL(n) (non-Archimedean case), inLie Group Representations II, College Park, Md., 1982/1983, Lecture Notes in Mathematics1041, Springer-Verlag, Berlin, 1984.
W. Casselman, H. Hecht and D. Miličié,Bruhat filtrations and Whittaker vectors for real groups, preprint.
N. Chen and H. Jacquet,Positivity of quadratic base change L functions, to appear in Bulletin de la Société Mathématique de France
W. Casselman and F. Shahidi,On irreducibility of standard modules for generic representations, Annales Scientifiques de l’École Normale Supérieure31 (1998), 561–589.
J. Dixmier and P. Malliavin,Factorizations de fonctions et vecteurs indéfiniment différentiables, Bulletin de la Société Mathématique de France102 (1978), 305–330.
Y. Flicker,Twisted tensors and Euler products, Bulletin de la Société Mathématique de France116 (1988), 295–313.
Y. Flicker,On distinguished representations, Journal für die reine und angewandte Mathematik418 (1991), 139–172.
Y. Flicker,Distinguished Representations and a Fourier Trace formula, Bulletin de la Société Mathématique de France120 (1992), 413–465.
Y. Flicker,Cyclic automorphic forms on a unitary group, Journal of Mathematics of Kyoto University37 (1997), 347–439.
Y. Flicker,Automorphic forms with anisotropic periods on a unitary group, Journal of Algebra220 (1999), 636–663.
Y. Flicker and D. Zinoniev,On the poles of twisted L-functions, Proceedings of the Japan Academy of Science71 (1995), 114–116.
F. Friedberg, S. Gelbart, H. Jacquet and J. Rogawski,Représentations génériques du groupe unitaire à trois variables, Comptes Rendus de l’Académie des Sciences, Paris, Série I329 (1999), 255–260.
S. Gelbart, J. Rogawski and D. Soudry,Endoscopy of cusp forms and algebraic cycles for U(3), Israel Journal of Mathematics83 (1993), 213–252.
S. Gelbart, J. Rogawski and D. Soudry,Endoscopy, theta liftings and period integrals for the unitary group in three variables, Annals of Mathematics145 (1997), 419–476.
I. M. Gelfand and D. Kazhdan,Representations of GL(n, K) where K is a local field, inLie Groups and their Representations (Proc. Summer School, Bolyai Janos Math. Soc., Budapest, 1971), Halsted, New York, 1975, pp. 95–118.
D. Goldberg,Some results on reducibility for unitary groups and local Asai L-functions, Journal für die reine und angewandte Mathematik448 (1994), 65–95.
G. Harder, R. P. Langlands and M. Rapoport,Algebraische Zyklen auf Hilbert-Blumenthal-Flächen (German) [Algebraic cycles on Hilbert-Blumenthal surfaces], Journal für die reine und angewandte Mathematik366 (1986), 53–120.
H. Jacquet,Generic representations, inNon-Commutative Harmonic Analysis, Actes Colloq., Marseille-Luminy, Lectures Notes in Mathematics587, Springer-Verlag, Berlin, 1977.
H. Jacquet,Relative Kloosterman Integrals for GL(3):II, Canadian Journal of Mathematics44 (1987), 117–155.
H. Jacquet,The continuous spectrum of the relative trace formula for GL(3)over a quadratic extension, Israel Journal of Mathematics89 (1995), 1–59.
H. Jacquet, E. M. Lapid and J. Rogawski,Periods of automorphic forms, Journal of the American Mathematical Society12 (1999), 173–240.
H. Jacquet and J. Shalika,On Euler products and the classification of automorphic representations I, II, American Journal of Mathematics103 (1981), 449–558 and 777–815.
S. Kudla, S. Rallis and S. Soudry,On the degree 5 L-function for Sp(2), Inventiones Mathematicae107 (1992), 483–541.
J. Kolk and V. S. Varadarajan,On the transverse symbol of vectorial distributions and some applications to harmonic analysis, Indagationes Mathematicae (N.S.)7 (1996), 67–96.
S. Lang,Algebraic Number Theory, Springer-Verlag, Berlin, 1986.
Mao, Z.,Relative Kloosterman integrals for the unitary group, Comptes Rendus de l’Académie des Sciences, Paris, Série I315 (1992), 381–386.
Z. Mao,Relative Kloosterman integrals for GL(3):III, Canadian Journal of Mathematics45 (1992), 1211–1230.
C. Moeglin and J. L. Waldspurger,Le spectre résiduel de GL(n), Annales Scientifiques de l’École Normale Supérieure22 (1989), 605–704.
J. Rogawski,Automorphic Representations of Unitary Groups in Three Variables, Annals of Mathematics Studies, No.123, Princeton University Press, 1990.
J. Rogawski,The multiplicity Theorem for A-packets, inThe Zeta Functions of Picard Modular Surfaces, Les publications CRM, Montreal, 1992.
F. Shahidi,Automorphic L-functions: a survey, inAutomorphic Forms, Shimura Varieties, and L-functions, Vol. I, Ann Arbor, MI, 1988, pp. 415–437.
F. Shahidi,A proof of Langlands’ conjecture on Plancherel measure; complementary series for p-adic groups, Annals of Mathematics132 (1990), 273–330.
F. Shahidi,On the Ramanujan conjecture and finiteness of poles for certain L-functions, Annals of Mathematics127 (1988), 547–584.
J. Shalika,The multiplicity one theorem for GL n,Annals of Mathematics100 (1974), 171–193.
N. Wallach,Real Reductive Groups II, Pure and Applied Mathematics, Vol. 132-II, Academic Press, Boston, 1992.
Y. Ye,Kloosterman integrals and base change, Journal für die reine und angewandte Mathematik400 (1989), 57–121.
Author information
Authors and Affiliations
Additional information
Partially supported by a Minerva grant.
Partially supported by NSF grant DMS 9619766 and 9988611.
Partially supported by NSF grant DMS 9700950.
Rights and permissions
About this article
Cite this article
Gelbart, S., Jacquet, H. & Rogawski, J. Generic representations for the unitary group in three variables. Isr. J. Math. 126, 173–237 (2001). https://doi.org/10.1007/BF02784154
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02784154