×
Jacquet, Hervé; Shalika, Joseph A.

A non-vanishing theorem for zeta functions of \(\mathrm{GL}_n\). (English) Zbl 0349.12006

Invent. Math. 38, 1-16 (1976).
Reviewer: Stephen Gelbart
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0349.12006

Cited in 4 Reviews
Cited in 53 Documents

MSC:

11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations
11F11 Holomorphic modular forms of integral weight
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings

Citations:

Zbl 0021.39201; Zbl 0205.50902; Zbl 0244.12011; Zbl 0367.10024; Zbl 0373.22008
PDF BibTeX XML Cite
\textit{H. Jacquet} and \textit{J. A. Shalika}, Invent. Math. 38, 1--16 (1976; Zbl 0349.12006)
Full Text: DOI EuDML
  • logo of hbz
  • logo of WorldCat

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
[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
[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) · Zbl 0244.12011
[6] Harish-Chandra: Automorphic forms on Semi-Simple Lie Groups. Springer Lecture Notes 62 (1968) · Zbl 0186.04702
[7] Jacquet, H.: Automorphic forms onGL(2). II. Springer Lecture Notes 278 (1972) · Zbl 0243.12005
[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 · Zbl 0356.12017
[9] Langlands, R. P.: On the functional equations satisfied by Eisenstein Series, preprint · Zbl 0332.10018
[10] Langlands, R. P.: Problems in the theory of automorphic forms. Modern Analysis and its applications. Springer Lecture Notes 170 (1970), pp. 18-61
[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) · Zbl 0205.50902
[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
[14] Rankin, R.: Contributions to the theory of Ramanujan’s functions ?(n) and similar arithmetical functions. I. Proc. Camb. Phil. Soc.35, 351-356 (1939) · Zbl 0021.39201
[15] Shalika, J.: The multiplicity one theorem forGL n . Annals of math., Vol. 100, No. 1, 171-193 (1974) · Zbl 0316.12010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.