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A non-vanishing theorem for zeta functions ofGL n

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References

  1. Andrianov, A. N.: On the Zeta-functions of the general linear groups. Congrès International des mathematiciens, pp. 273–276. Paris: Gauthier-Villars 1970

    Google Scholar 

  2. Gelfand, I. M., Kajdan, D. A.: Representations of the groupGL (n, K) whereK is a local field. Lie groups and their representations, Summer School of Group Representations, Budapest, pp. 95–118. New York: Halsted-Press 1971

    Google Scholar 

  3. Godement, R.: Analyse spectrale des fonctions modulaires. Séminaire Bourbaki, (1964/65), No. 278, 26 p.

  4. Godement, R.: Introduction à la théorie de Langlands. Séminaire Bourbaki, (1966/67), No. 321, 30 p.

  5. Godement, R., Jacquet, H.: Zeta functions of simple algebras. Springer Lecture Notes 260 (1972)

  6. Harish-Chandra: Automorphic forms on Semi-Simple Lie Groups. Springer Lecture Notes 62 (1968)

  7. Jacquet, H.: Automorphic forms onGL(2). II. Springer Lecture Notes 278 (1972)

  8. Jacquet, H., Pyatetskii-Shapiro, I. I., Shalika, J.: Construction de formes automorphes pour le groupeGL(3). Comptes Rendus, Acad. Sci., Paris, Vol. 282, (1976), pp. 91–94

    Google Scholar 

  9. Langlands, R. P.: On the functional equations satisfied by Eisenstein Series, preprint

  10. Langlands, R. P.: Problems in the theory of automorphic forms. Modern Analysis and its applications. Springer Lecture Notes 170 (1970), pp. 18–61

    Google Scholar 

  11. Langlands, R. P.: Euler products. Lecture notes, Yale University (1967)

  12. Ogg, A. P.: On a convolution ofL-series. Inventiones Math.,7, 297–312 (1969)

    Google Scholar 

  13. Pyatetskii-Shapiro, I.: Euler subgroups, Lie groups and their representations. Summer School of Group Representations, Budapest, pp. 597–620. New York: Halsted-Press 1971

    Google Scholar 

  14. Rankin, R.: Contributions to the theory of Ramanujan's functions τ(n) and similar arithmetical functions. I. Proc. Camb. Phil. Soc.35, 351–356 (1939)

    Google Scholar 

  15. Shalika, J.: The multiplicity one theorem forGL n . Annals of math., Vol. 100, No. 1, 171–193 (1974)

    Google Scholar 

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To R. Godement

Partially supported by N.S.F. Grant MPS75-08545

Partially supported by N.S.F. Grant MPS71-03321

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Jacquet, H., Shalika, J.A. A non-vanishing theorem for zeta functions ofGL n . Invent Math 38, 1–16 (1976). https://doi.org/10.1007/BF01390166

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