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References
[Ariturk] Ariturk, H.: On the composition series of principal series representations of a 3-fold covering group ofSL(2,k), preprint, 1978
[BoJa] Borel, A., Jacquet, H.: Automorphic forms and automorphic representations. In: Proc. Symp. Pure Math., Vol. 33, Part 1, pp. 189–202. A.M.S. 1979
[De] Deligne, P.: Formes modularies et représentations deGL 2. In: Springer Lecture Notes, Vol. 349, 1973
[De2] Deligne, P.: La Conjecture de Weil, I. Pub. I.H.E.S.,43, 273–307 (1974)
[De3] Deligne, P.: Sommes de Gauss Cubiques et Revêtements deSL(2). Séminaire Bourbaki, No. 539, 1978/79
[Flick] Flicker, Y.: Automorphic forms on covering groups ofGL(2). Invent. Math. in press (1980)
[Ge] Gelbart, S.: Weil's Representation and the Spectrum of the Metaplectic Group. Springer Lecture Notes, Vol. 530, 1976
[GeHPS] Gelbart, S., Howe, R., Piatetski-Shapiro, I.: Existence and Uniqueness of Whittaker Models for the Metaplectic Group. Israel J. Math. Vol. 34 (1979)
[GePS] Gelbart, S., Piatetski-Shapiro, I.: On Shimura's correspondence for modular forms of half-integral weight. In: Proceedings, Colloquium on Automorphic Forms, Representation Theory and Arithmetic, Bombay, 1979
[GeSa] Gelbart, S., Sally, P.J.: Intertwining operators and automorphic forms for the metaplectic group. P.N.A.S., U.S.A.,72, 1406–1410 (1975)
[Go] Godement, R.: Notes on Jacquet-Langlands Theory. Institute for Advanced study, Princeton, 1970
[GGPS] Gelfand, I., Graev, M., Piatetski-Shapiro, I.: Representation Theory and Automorphic Functions. Philadelphia: W.B. Saunders Co. 1969
[Go2] Godement, R.: Travaux de Hecke II. Séminaire Bourbaki, No. 59, 1951/1952
[Hecke] Hecke, E.: Mathematische Werke, Göttingen, 1959
[Ho] Howe, R.: θ-series and automorphic forms. In: Proceedings of Symposia in Pure Math. Vol. 33, Part 1, pp. 275–286, A.M.S., 1979
[Ja] Jacquet, H.: Automorphic Forms onGL(2): Part II. Springer Lecture Notes, Vol. 278, 1972
[JL] Jacquet, H., Langlands, R.P.: Automorphic Forms onGL(2). Springer Lecture Notes, Vol. 114, 1970
[Kubota] Kubota, T.: Automorphic functions and the Reciprocity Law in a Number Field, Kyoto Univ. Press, 1969
[Kub2] Kubota, T.: Some Number-Theoretical Results on Real Analytic Automorphic Forms. In: Lecture Notes in Mathematics, Vol. 185, 87–96, Springer-Verlag 1971
[La] Langlands, R.P.: Automorphic Representations, Shimura Varieties, and motives: Ein Märchen. In: Proc. Symp. Pure Math., Vol. 33, Part 2, 204–246. A.M.S., 1979
[Mackey] Mackey, G.: Unitary representations of group extensions I. Acta Math.99, 265–311 (1958)
[Mackey 2] Mackey, G.: Induced Representations of Locally Compact Groups and Applications. In: Functional Analysis and Related Fields (F. Browder, ed.). Berlin-Heidelberg-New York: Springer-Verlag 1970
[MOS] Magnus, W., Oberhettinger, F., Soni, R.: Formulas and Theorems for the Special Functions of Mathematical Physics. New York: SpringerVerlag 1966
[Mei] Meister, J.: Cornell University Thesis, 1979
[Moen] Moen, C.: Univ. of Chicago Thesis, 1979
[Moore] Moore, C.: Group extensions ofp-adic linear groups. Pub. I.H.E.S., No. 35, 1968
[Niwa] Niwa, S.: Modular forms of half-integral weight and the integral of certain functions. Nagoya J. Math.56, 147–161 (1975)
[Patt] Patterson, S.J.: A cubic analogue of the theta-series, I, II, J. Crelle 296, 125–161 and 217–220 (1977)
[PS] Piatetski-Shapiro, I.I.: Distinguished representations and Tate Theory for a reductive group. Proceedings. ICM, Helsinki, 1978
[RS] Rallis, S., Schiffmann, G.: Représentations supercuspidales de groupe métaplectique, J. Math. Kyoto Univ., 17, 143–179 (1977)
[Se-St] Serre, J-P., Stark, H.: Modular forms of weight 1/2. In: Springer Lecture Notes, Vol. 627, 1977
[Shalika] Shalika, J.: Representations of the two-by-two unimodular group over local fields. Thesis, Johns Hopkins, University, 1966
[Sha-Tan] Shalika, J., Tanaky, S.: On an explicit construction of a certain class of automorphic forms. Amer. J. Math.91, 1043–1076 (1969)
[Shim] Shimura, G.: On modular forms of half-integral weight. Ann. Math.97, 440–481 (1973)
[Shin] Shintani, T.: On the construction of holomorphic cusp forms of half-integral weight. Nagoya Math. J.58, 83–126 (1975)
[Tate] Tate, J.: On Fourier analysis in number fields and Hecke's zeta functions. In: Algebraic Number Theory (J. Cassels and A. Fröhlich, eds.). Washington D.C.: Thompson Publishing Co. 1967
[Vignéras] Vignéras, M.-F.: Facteurs gamma et équations fonctionnelles. In: Springer Lecture Notes, Vol. 627, 1977
[Wald] Waldspurger, J.L.: Correspondances de Shimura et Shintani, preprint, 1979
[We] Weil, A.: Sur certains groups d'opératuers unitaires. Acta Math.111, 143–211 (1964)
[WeB] Weil, A.: Zeta-functions and distributions. Seminaire Bourbaki, No. 312, 1965–1966
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Gelbart, S., Piatetski-Shapiro, I.I. Distinguished representations and modular forms of half-integral Weight. Invent Math 59, 145–188 (1980). https://doi.org/10.1007/BF01390042
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DOI: https://doi.org/10.1007/BF01390042