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Automorphic forms of low rank

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 880))

Research partially supported by NSF grant MCS79-05018.

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Bibliography

  1. A. Borel, Introduction to Automorphic Forms, Proc. Symp. Pure Math., v. IX, A.M.S., Providence, R. I., 1966, 199–210.

    Google Scholar 

  2. A. Borel, Reduction Theory for Arithmetic Groups, Proc. Symp. Pure Math., v. IX, A.M.S., Providence R. I., 1966, 20–25.

    Google Scholar 

  3. P. Cartier, Representations of p-adic groups: A survey, Proc. Symp. Pure Math., v. XXXIII, A.M.S., Providence, R. I., 1979, 111–156.

    Google Scholar 

  4. J. Dixmier and P. Malliavin, Factorisations de fonctions et vecteurs indéfiniment differentiables, Pub. Math. de l'Univ. P.et M. Curie, no. 7.

    Google Scholar 

  5. S. Gelbart, Examples of dual reductive pairs, Proc. Symp. Pure Math., v. XXXIII, A.M.S., Providence, R. I., 1979.

    Google Scholar 

  6. S. Gelbart and I. Piatetski-Shapiro, Distinguished Representations and Modular Forms of Half-integral Weight, Inv. Math. 59 (1980), 145–188.

    Article  MathSciNet  MATH  Google Scholar 

  7. K. Gross and R. Kunze, Bessel functions and representation theory, II, J. Fun. Anal. 25(1977), 1–49.

    Article  MathSciNet  MATH  Google Scholar 

  8. Harish-Chandra, Automorphic forms on semi-simple Lie groups, Notes by J. G. M. Mars, Lecture Notes in Math. 68, Springer-Verlag, Heidelberg, New York, 1968.

    Chapter  Google Scholar 

  9. R. Howe, A notion of rank for unitary representations of classical groups, C.I.M.E. Summer School on Harmonic Analysis, Cortona, 1980, to appear.

    Google Scholar 

  10. R. Howe, ϑ-series and invariant theory. Proc. Symp. Pure Math., v. XXXIII, A.M.S., Providence, R. I., 1979, 275–286.

    Google Scholar 

  11. R. Howe, Basic properties of the oscillator representation, in preparation.

    Google Scholar 

  12. N. Jacobson, Lie Algebras, Wiley-Interscience, New York, 1962.

    MATH  Google Scholar 

  13. M. Kashiwara and M. Vergne, On the Siegel-Shale-Weil representation and harmonic polynomials, Inv. Math.

    Google Scholar 

  14. M. Kneser, Strong Approximation, Proc. Symp. Pure Math., v. IX, A.M.S., Providence, R.I., 1966, 187–196.

    Google Scholar 

  15. H. Maass, Siegel's Modular Forms and Dirichlet Series, Lecture Notes in Math. 216, Springer, Heidelberg, New York, 1971.

    MATH  Google Scholar 

  16. I. Piatetski-Shapiro, Multiplicity One Theorems, Proc. Symp. Pure Math. XXXIII, A.M.S., Providence, R.I., 1979, 209–212.

    Google Scholar 

  17. S. Rallis, Langland's Functoriality and the Weil Representation, preprint.

    Google Scholar 

  18. H. Resnikoff, On singular automorphic forms in several complex variables, Am. J. Math. 95 (1973), 321–332.

    Article  MathSciNet  MATH  Google Scholar 

  19. J. P. Serre and S. Stark, Modular forms of weight 1/2, Springer Lecture Notes 627, Springer-Verlag 1977.

    Google Scholar 

  20. A. Weil, Basic Number Theory, 2nd Ed., Grundlehren der Math. Wiss. 144, Springer, Heidelberg, New York, 1973.

    Book  MATH  Google Scholar 

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Jacques Carmona Michèle Vergne

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© 1981 Springer-Verlag

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Howe, R. (1981). Automorphic forms of low rank. In: Carmona, J., Vergne, M. (eds) Non Commutative Harmonic Analysis and Lie Groups. Lecture Notes in Mathematics, vol 880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090411

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  • DOI: https://doi.org/10.1007/BFb0090411

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  • Print ISBN: 978-3-540-10872-6

  • Online ISBN: 978-3-540-38783-1

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