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Automorphic forms on covering groups of GL(2). (English) Zbl 0431.10014

MSC:
11F70 Representation-theoretic methods; automorphic representations over local and global fields
11F11 Holomorphic modular forms of integral weight
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
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References:
[1] Deligne, P.: Sommes de Gauss cubiques et revêtements deSL(2) (d’après S.J. Patterson). Sém. Bourbaki, Juin 1979
[2] Gelbart, S.: Weil’s Representation and the Spectrum of the Metapletic Group. Springer Lecture Notes 530, 1976 · Zbl 0365.22017
[3] Gelbart, S., Jacquet, H.: Forms ofGL(2) from the analytic point of view. Proc. Symp. Pure Math.33, 1979 · Zbl 0409.22013
[4] Gelbart, S., Piatetski-Shapiro, I.: Distinguished representations and modular forms of halfintegral weight. preprint · Zbl 0426.10027
[5] Gelbart, S., Piatetski-Shapiro, I.: On Shimura’s correspondence for modular forms of halfintegral weight. Proc. Int. Coll. Auto. Forms. Rep. Theory and Arith., Bombay 1980 · Zbl 0426.10027
[6] Harish-Chandra: Harmonic analysis on reductivep-adic groups. Springer Lecture Notes 162, 1970 · Zbl 0202.41101
[7] Harish-Chandra: Harmonic analysis on reductivep-adic groups. Proc. Symp. Pure Math.26, 167-192 (1973) · Zbl 0289.22018
[8] Jacquet, H., Langlands, R.P.: Automorphic forms onGL(2). Springer Lecture Notes 114, 1970 · Zbl 0236.12010
[9] Kubota, T.: Automorphic functions and the reciprocity law in a number field, mimeographed notes. Kyoto Univ. 1969 · Zbl 0231.10017
[10] Langlands, R.P.: Base change forGL(2), preprint, Inst. Advanced Study 1975
[11] Labesse, J.P., Langlands, R.P.:L-indistinguishability forSL(2) Can. J. Math.31, 726-785 (1979) · Zbl 0421.12014
[12] Moore, C.: Group extensions ofp-adic linear groups. Publ. Math. I.H.E.S.35, 157-222 (1968)
[13] Rallis, S., Schiffmann: Représentations supercuspidales du groupe métaplectique. J. Math. Kyoto Univ.,17, 567-603 (1977) · Zbl 0398.22023
[14] Serre, J-P., Stark, H.: Modular forms of weight 1/2. Springer Lecture Notes 627, 29-67 (1977)
[15] Shimura, G.: On modular forms of half-integral weight. Ann. Math.97, 440-481 (1973) · Zbl 0266.10022
[16] Shintani, T.: On construction of holomorphic cusp forms of half-integral weight. Nagoya Math. J.,58, 83-126 (1975) · Zbl 0316.10016
[17] Weil, A.: Sur certains groupes d’opérateurs unitaires. Acta Math.,111, 143-211 (1964) · Zbl 0203.03305
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