Document Zbl 0515.10024

On the Saito-Kurokawa lifting. (English) Zbl 0515.10024

Invent. Math. 71, 309-338 (1983).

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MSC:

11F27	Theta series; Weil representation; theta correspondences
11F70	Representation-theoretic methods; automorphic representations over local and global fields
11R39	Langlands-Weil conjectures, nonabelian class field theory
22E55	Representations of Lie and linear algebraic groups over global fields and adèle rings

Keywords:

Saito-Kurokawa lifting; automorphic forms; Weyl representation; description of counterexamples; generalized Ramanujan conjecture

Citations:

Zbl 0505.12017

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Full Text: DOI EuDML

References:

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[2]	Howe, R., Piatetski-Shapiro, I.: A counterexample to the ?generalized Ramanujan conjecture? for (quasi-) spilt groups. Proc. of Symposium in Pure Math.33, (part 1) 315-322 (1979) · Zbl 0423.22018
[3]	Rallis, S.: Langlands’ functortiality and the Weil representation (preprint) · Zbl 0532.22016
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[6]	Piatetski-Shapiro, I.: L-functions forGSp 4 (preprint)
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[8]	Jacquet, H., Langlands R.: Automorphic forms onGL(2). Lecture Notes, vol. 114. Berlin-Heidelberg-New York, Springer · Zbl 0236.12010
[9]	Piatetski-Shapiro, I.: Multiplicity one theorems. Proc. of Symposia in Pure Math.33, (part 1) 209-212 (1979) · Zbl 0423.22017
[10]	Waldspurger, J.L.: Sur les Coefficients de Fourier des Formes Modulaires de poids demi-entier. J. Math. Pure Appl60, 345-484 (1981) · Zbl 0431.10015
[11]	Kurokawa, N.: Examples of eigenvalues of Hecke operators on Siegel cusp forms of degree two. Invent. Math.49, 149-165 (1978) · Zbl 0397.10018 · doi:10.1007/BF01403084
[12]	Maass, H.: I. Über eine Spezialschar von Modulformen Zweiten Grades. Invent. Math.52, 95-104 (1979) · doi:10.1007/BF01389857
[13]	Maass, H.: II. Über eine Spezialschar von Modulformen Zweiten Grades. Invent. Math.53, 249-253 (1979) · Zbl 0413.10021 · doi:10.1007/BF01389765
[14]	Maass, H.: III. Über eine Spezialschar von Modulformen Zweiten Grades. Invent. Math.53, 255-265 (1979) · doi:10.1007/BF01389766
[15]	Andrianov, A.: Modular descent and the Saito-Kurokawa conjecture. Invent. Math.53, 267-280 (1980) · Zbl 0414.10017 · doi:10.1007/BF01389767
[16]	Langlands, R.: On the notion of an automorphic representation. Proc. of Symp. in Pure Math.33, (part 1) 203-208 (1979) · Zbl 0414.22021
[17]	Jacquet, H., Shalika, J.: On Euler products and the classification of automorphic forms. Amer. J. of Math.103, 499-558 (1981) · Zbl 0473.12008 · doi:10.2307/2374103
[18]	Waldspurger, J.L.: Correspondances de Shimura et quaternions. (preprint) · Zbl 0724.11026
[19]	Borel, A., Jacquet, H.: Automorphic forms and automorphic representations. Proc. of Symp. in Pure Math.33, (part 1) 189-202 (1979) · Zbl 0414.22020
[20]	Andrianov, A.N.: Dirichlet series and Euler product in the theory of Siegel modular forms of genus 2. MUAH, CCCP 112, (1971)
[21]	Langlands, R.P.: Euler products. Yale Univ. Press., 1971 · Zbl 0231.20017
[22]	Howe, R.: I. Piatetski-Shapiro. Some examples of automorphic forms onSp 4. Duke Math. Jour. (to appear) · Zbl 0529.22012
[23]	Gelbart, S.: Piatetski-Shapiro, Distinguished representations and modular forms of half-integral weight. Invent. Math.59, 145-188 (1980) · Zbl 0426.10027 · doi:10.1007/BF01390042
[24]	Gelbart, S.: Weil’s representation and the spectrum of the Metaplectic Group. Lecture Notes, vol 530 Berlin-Heidelberg-New York: Springer · Zbl 0365.22017
[25]	Rallis, S.: On the Howe duality conjecture. Preprint · Zbl 0624.22011
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[27]	Piatetski-Shapiro, I., Soudry, L.: ? Factors forGPp 4. Journal of Faculty of Sci. Tokyo Sec IA (Vol 28, No 3) · Zbl 0499.22020
[28]	Gelbart, S., Piatetski-Shapiro, I.: Some remarks on Metaplectic Cusp Forms and the Corespondence of Shimura and Waldspurger. Israel J. of Math, (to appear) · Zbl 0526.10026

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