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Mellin transforms of Whittaker functions onGL(4,ℝ) andGL(4,ℂ)

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References

  1. Appell, P., Kampé de Fériet, J.: Fonctions hypergéometriques et hypersphériques. Gauthier-Villars, Paris, 1926

    MATH  Google Scholar 

  2. Bailey, W.N.: Generalized hypergeometric series. Cambridge University Press, Cambridge, 1935

    MATH  Google Scholar 

  3. Bump, D.: Automorphic forms onGL(3,ℝ). Springer Lecture Notes in Mathematics #1083 Springer-Verlag, New York, 1984

    MATH  Google Scholar 

  4. Bump, D, Barnes’ second lemma and its application to Rankin-Selberg convolutions. American Journal of Mathematics110 (1988) #1 179–185

    Article  MATH  MathSciNet  Google Scholar 

  5. Bump, D.: The Rankin Selberg method: a survey. In: Number theory, trace formulas, and discrete groups (Oslo, 1987). Academic Press, New York, 1989

    Google Scholar 

  6. Bump, D., Friedberg, S.: The exterior square automorphicL-functions onGL(n). In: Festschrift in honor of I. I. Piatetski-Shapiro on the occasion of his sixtieth birthday, Part II (Ramat Aviv, 1989), Israel Math Conf. Proc. 3, Weizmann, Jerusalem, 1990

    Google Scholar 

  7. Bump, D., Friedberg, S.: On Mellin transforms of unramified Whittaker functions onGL(3,ℂ). J. Math. Anal. Appl.139 (1989) #1 205–216

    Article  MATH  MathSciNet  Google Scholar 

  8. Bump, D., Hoffstein, J.: Cubic metaplectic forms on GL(3). Inventiones Math.84 (1986) 481–505

    Article  MATH  MathSciNet  Google Scholar 

  9. Friedberg, S., Goldfeld, D.: Mellin transforms of Whittaker functions (to appear).

  10. Godement, R., Jacquet, H.: Zeta Functions of Simple Algebras, Springer Lecture Notes in Mathematics #260, Springer-Verlag, New York, 1962

    Google Scholar 

  11. Gradshteyn, I., Ryzhik, I.: Tables of Integrals, Series, and Products, Corrected and Enlarged Edition. Academic Press, New York, 1980

    Google Scholar 

  12. Hashizume, M.: Whittaker functions on semisimple Lie groups. Hiroshima Math. J.12 (1982) 259–293

    MATH  MathSciNet  Google Scholar 

  13. Jacquet, H.: Fonctions de Whittaker associées aux groupes de Chevalley. Bull. Soc. Math. France95 (1967) 243–309

    MATH  MathSciNet  Google Scholar 

  14. Kostant, B.: On Whittaker vectors and representation theory. Inventiones Math.48 (1978) 101–184

    Article  MATH  MathSciNet  Google Scholar 

  15. Piatetski-Shapiro, I. I.: Euler subgroups. In: Lie groups and their representations. John Wiley and Sons, New York, 1975

    Google Scholar 

  16. Selberg, A.: Harmonic analysis and discontinous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series. J. Indian Math. Soc.20 (1956) 47–87

    MathSciNet  Google Scholar 

  17. Shalika, J.: The multiplicity one theorem forGL(n). Annals of Math100 (1974) 171–193

    Article  MathSciNet  Google Scholar 

  18. Slater, L.: Generalized hypergeometric functions. Cambridge University Press, Cambridge, 1966

    MATH  Google Scholar 

  19. Stade, E.: Poincaré series and Whittaker functions forGL(3,ℂ). Ph.D. Thesis, Columbia University, 1988

  20. Stade, E.: On explicit integral formulas forGL(n,ℝ)-Whittaker functions. Duke Mathematical Journal60 (1990) #2 2313–362

    MathSciNet  Google Scholar 

  21. Stade, E.:GL(4,ℝ)-Whittaker functions and4 F 3(1) hypergeometric series. Trans. Amer. Math. Soc.336 (1993) #1 253–264

    Article  MATH  MathSciNet  Google Scholar 

  22. Stade, E.: Hypergeometric series and Euler factors at infinity forL-functions onGL(3,ℝ)·GL(3,ℝ). American Journal of Mathematics115 (1993) #2 371–387

    Article  MATH  MathSciNet  Google Scholar 

  23. Varadarajan, V. S.: Lie Groups, Lie Algebras, and Their Representations. Springer-Verlag, New York, 1984

    MATH  Google Scholar 

  24. Wallach, N.: Asymptotic expansions of generalized matrix coefficients of representations of real reductive groups. Springer Lecture Notes in Mathematics #1024, Springer-Verlag, New York, 1983

    Google Scholar 

  25. Whittaker, E., Watson, G.: A course of modern analysis. Cambridge University Press, Cambridge, 1902

    MATH  Google Scholar 

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Supported in part by NSF grant #DMS-9400324

This article was processed by the author using the Springer-Verlag TEX P Jourlg macro package 1991

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Stade, E. Mellin transforms of Whittaker functions onGL(4,ℝ) andGL(4,ℂ). Manuscripta Math 87, 511–526 (1995). https://doi.org/10.1007/BF02570491

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