Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Casselman, W., and Shalika, J., "The unramified principal series of p-adic groups II: The Whittaker function", Compositio Math., Vol. 41, Fasc. 2 (1980), pp.207–231.
Flicker, Y., "L-packets and liftings for U(3)", preprint, Princeton University, 1982.
Gelbart, S., "Examples of dual reductive pairs", in Proceedings of Symposia in Pure Mathematics, Vol. 33 (1979), part 1, pp.287–296, Amer. Math. Soc.
Gelbart, S., and Piatetski-Shapiro, I., "On Shimura's correspondence for modular forms of half-integral weight", in Automorphic Forms, Representation Theory and Arithmetic (Bombay, 1979), pp.1–39, Tata Inst. Fund. Res. Studies in Math., 10, Tata Inst. Fund. Res., Bombay, 1981.
Godement, R., and Jacquet, H., Zeta Functions of Simple Algebras, Springer Lecture Notes in Mathematics, Vol. 260, 1972.
Goldstein, Larry, Analytic Number Theory, Prentice-Hall, 1971.
Howe, R., "θ-series and automorphic forms", in Proceedings of Symposia in Pure Mathematics, Vol. 33 (1979), part 1, pp.275–286, Amer. Math. Soc.
Howe, R., and Piatetski-Shapiro, I., "A counterexample to the "Generalized Ramanujan Conjecture" for (quasi-) split groups", in Proceedings of Symposia in Pure Mathematics, Vol. 33 (1979), part 1, pp.315–322, Amer. Math. Soc.
__________, "Some examples of automorphic forms on SP4", Duke Math. Journal, to appear.
Jacquet, H., Automorphic Forms on GL(2): II, Springer Lecture Notes in Mathematics, No. 278, 1972.
Jacquet, H., and R. P. Langlands, Automorphic Forms on GL(2), Lecture Notes in Math., Vol. 114, Springer, 1970.
Jacquet, H., Piatetski-Shapiro, I., and Shalika, J., "Automorphic forms on GL(3): I and II", Annals of Math., 109 (1979), pp.169–258.
Kazhdan, D., "Some applications of the Weil representation", Journal d'Analyse Mathématique, Vol. 32 (1977), pp.235–248.
Keys, D., Principal series representations of special unitary groups over local fields, preprint, U. of Utah, 1981.
Kottwitz, R., Unpublished notes.
Kudla, S., "On certain arithmetic automorphic forms for SU(1,q)", Inventiones Math. 52, pp.1–25 (1979).
_____, "On certain Euler products for SU(2,1)", Compositio Math., Vol. 42, Fasc. 3, 1981, pp.321–344.
Langlands, R. P., "Problems in the theory of automorphic forms", Lectures in Modern Analysis and Applications, Lecture Notes in Mathematics, Vol. 170, Springer, New York, 1970, pp.18–86.
Novodvorsky, M., "Automorphic L-functions for the symplectic group GSp4", in Proceedings of Symposia in Pure Mathematics, Vol. 33 (1979), part 2, pp.87–96, Amer. Math. Soc.
Piatetski-Shapiro, I., "Tate theory for reductive groups and distinguished representations", in Proceedings of the International Congress of Mathematicians, Helsinki 1978, pp.585–590.
________, "L-functions for GSp4", preprint, 1981.
________, Lecture notes, Yale University, 1977–78.
________, "On the Saito-Kurokawa lifting", Inventiones Math., to appear.
________, and Soudry, D., "L and ε factors for GSp(4)", Jour. Fac. Science, Univ. Tokyo, Sec. 1A, Vol. 28, No.3 (Shintani Memorial Volume), pp.505–530, Feb. 1982.
Rallis, S., "Langlands' functoriality and the Weil representation", Amer. J. Math., Vol. 104, No. 3, 1982, pp.469–515.
Rankin, R., "Contributions to the theory of Ramanujan's function Ï„(n) and similar arithmetical functions", Proc. Cam. Phil. Soc., 1939.
Rogawski, J., preprint, Yale Univ., 1981.
Selberg, A., Bemerkungen über eine Dirichletsche Reihe, die mit der Theorie der Modulformen naheverbunden ist, Ach. Math. Naturvid. 43 (1940), pp.47–50.
Shalika, J., "The multiplicity one theorem for GLn", Annals of Math. 100 (1974), pp.171–193.
_____, and Tanaka, S., "On an explicit construction of a certain class of automorphic forms", Amer. J. Math. 91 (1969), pp.1049–1076.
Shimura, G., "On modular forms of half-integral weight", Annals of Math. (2) 19 (1973), pp.440–481.
Shintani, T., "On automorphic forms on unitary groups of order 3", preprint 1979.
Tate, J., "On Fourier analysis in number fields and Hecke's zetafunctions", in Algebraic Number Theory, Cassels, J. W. S. and A. Fröhlich, eds. Thompson Publishing Co., Washington, D.C., 1967, pp.305–347.
Waldspurger, J.-L., "Correspondance de Shimura", J. Math. Pures et Appl. 59 (1980), pp.1–133.
________, "Correspondances de Shimura et Quaternions", preprint, Paris, 1981.
Weil, A., "Sur certains groupes d'operateurs unitaires, Acta Math. 111 (1964), 143–211.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
Gelbart, S., Piatetski-Shapiro, I. (1983). Automorphic forms and L-functions for the unitary group. In: Herb, R., Kudla, S., Lipsman, R., Rosenberg, J. (eds) Lie Group Representations II. Lecture Notes in Mathematics, vol 1041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073147
Download citation
DOI: https://doi.org/10.1007/BFb0073147
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12715-4
Online ISBN: 978-3-540-38699-5
eBook Packages: Springer Book Archive