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Automorphic forms and L-functions for the unitary group

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Lie Group Representations II

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References

  1. 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.

    MathSciNet  MATH  Google Scholar 

  2. Flicker, Y., "L-packets and liftings for U(3)", preprint, Princeton University, 1982.

    Google Scholar 

  3. 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.

    Article  MathSciNet  MATH  Google Scholar 

  4. 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.

    Chapter  Google Scholar 

  5. Godement, R., and Jacquet, H., Zeta Functions of Simple Algebras, Springer Lecture Notes in Mathematics, Vol. 260, 1972.

    Google Scholar 

  6. Goldstein, Larry, Analytic Number Theory, Prentice-Hall, 1971.

    Google Scholar 

  7. 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.

    Article  MathSciNet  Google Scholar 

  8. 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.

    Article  MathSciNet  MATH  Google Scholar 

  9. __________, "Some examples of automorphic forms on SP4", Duke Math. Journal, to appear.

    Google Scholar 

  10. Jacquet, H., Automorphic Forms on GL(2): II, Springer Lecture Notes in Mathematics, No. 278, 1972.

    Google Scholar 

  11. Jacquet, H., and R. P. Langlands, Automorphic Forms on GL(2), Lecture Notes in Math., Vol. 114, Springer, 1970.

    Google Scholar 

  12. Jacquet, H., Piatetski-Shapiro, I., and Shalika, J., "Automorphic forms on GL(3): I and II", Annals of Math., 109 (1979), pp.169–258.

    Article  MathSciNet  MATH  Google Scholar 

  13. Kazhdan, D., "Some applications of the Weil representation", Journal d'Analyse Mathématique, Vol. 32 (1977), pp.235–248.

    Article  MathSciNet  MATH  Google Scholar 

  14. Keys, D., Principal series representations of special unitary groups over local fields, preprint, U. of Utah, 1981.

    Google Scholar 

  15. Kottwitz, R., Unpublished notes.

    Google Scholar 

  16. Kudla, S., "On certain arithmetic automorphic forms for SU(1,q)", Inventiones Math. 52, pp.1–25 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  17. _____, "On certain Euler products for SU(2,1)", Compositio Math., Vol. 42, Fasc. 3, 1981, pp.321–344.

    MathSciNet  MATH  Google Scholar 

  18. 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.

    Chapter  Google Scholar 

  19. 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.

    Article  MathSciNet  Google Scholar 

  20. Piatetski-Shapiro, I., "Tate theory for reductive groups and distinguished representations", in Proceedings of the International Congress of Mathematicians, Helsinki 1978, pp.585–590.

    Google Scholar 

  21. ________, "L-functions for GSp4", preprint, 1981.

    Google Scholar 

  22. ________, Lecture notes, Yale University, 1977–78.

    Google Scholar 

  23. ________, "On the Saito-Kurokawa lifting", Inventiones Math., to appear.

    Google Scholar 

  24. ________, 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.

    MathSciNet  MATH  Google Scholar 

  25. Rallis, S., "Langlands' functoriality and the Weil representation", Amer. J. Math., Vol. 104, No. 3, 1982, pp.469–515.

    Article  MathSciNet  MATH  Google Scholar 

  26. Rankin, R., "Contributions to the theory of Ramanujan's function Ï„(n) and similar arithmetical functions", Proc. Cam. Phil. Soc., 1939.

    Google Scholar 

  27. Rogawski, J., preprint, Yale Univ., 1981.

    Google Scholar 

  28. Selberg, A., Bemerkungen über eine Dirichletsche Reihe, die mit der Theorie der Modulformen naheverbunden ist, Ach. Math. Naturvid. 43 (1940), pp.47–50.

    MathSciNet  MATH  Google Scholar 

  29. Shalika, J., "The multiplicity one theorem for GLn", Annals of Math. 100 (1974), pp.171–193.

    Article  MathSciNet  MATH  Google Scholar 

  30. _____, and Tanaka, S., "On an explicit construction of a certain class of automorphic forms", Amer. J. Math. 91 (1969), pp.1049–1076.

    Article  MathSciNet  MATH  Google Scholar 

  31. Shimura, G., "On modular forms of half-integral weight", Annals of Math. (2) 19 (1973), pp.440–481.

    Article  MathSciNet  MATH  Google Scholar 

  32. Shintani, T., "On automorphic forms on unitary groups of order 3", preprint 1979.

    Google Scholar 

  33. 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.

    Google Scholar 

  34. Waldspurger, J.-L., "Correspondance de Shimura", J. Math. Pures et Appl. 59 (1980), pp.1–133.

    MathSciNet  MATH  Google Scholar 

  35. ________, "Correspondances de Shimura et Quaternions", preprint, Paris, 1981.

    Google Scholar 

  36. Weil, A., "Sur certains groupes d'operateurs unitaires, Acta Math. 111 (1964), 143–211.

    Article  MathSciNet  MATH  Google Scholar 

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Rebecca Herb Stephen Kudla Ronald Lipsman Jonathan Rosenberg

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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

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  • DOI: https://doi.org/10.1007/BFb0073147

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