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Holomorphic Siegel modular forms associated to \(SO(n,1)\). (English) Zbl 0465.10020


MSC:

11F27 Theta series; Weil representation; theta correspondences
11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
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References:

[1] Andrianov, A.N., Maloletkin, G.N.: Behavior of theta series of degreen under modulat substitutions. Math. USSR Izv,39, 227-241 (1975) · Zbl 0326.10025 · doi:10.1070/IM1975v009n02ABEH001474
[2] Borel, A.: Introduction aux groupes arithmetiques. Paris: Hermann 1969 · Zbl 0186.33202
[3] Gelbart, S.: Holomorphic discrete series for the real symplectic group. Invent. Math.19, 49-58 (1973) · Zbl 0236.22013 · doi:10.1007/BF01418850
[4] Hecke, E.: Zur Theorie der elliptischen Modulfunktionen. Math. Ann.97, 210-242 (1926) · JFM 52.0377.04 · doi:10.1007/BF01447866
[5] Howe, R.: ?-series and invariant theory. Proc. Symp. Pure Math.33, 275-285 (1979) · Zbl 0423.22016
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[7] Kudla, S., Millson, J.: Geodesic cycles and the Weil representation, quotients of hyperoclic space and Siegel modular forms. Preprint (1979) · Zbl 0495.10016
[8] Millson, J., Raghunathan, M.S.: Geometric construction of cohomology for arithmetic groups I. Papers Dedicated to the Memory of V.K. Patodi. Bangalore: Indian Academy of Sciences
[9] Siegel, C.L.: Indefinite quadratische Formen und Funktionen Theorie. I. Math. Ann.124, 17-54 (1951) · Zbl 0043.27402 · doi:10.1007/BF01343549
[10] Shintani, T.: On construction of holomorphic cusp forms of half-integral weight. Nagoya Math. J.58, 83-126 (1975) · Zbl 0316.10016
[11] Weil, A.: Elliptic functions according to Eisenstein and Kronecker. Ergebnisse der Mathematik. Vol. 88, Berlin, Heidelberg, New York: Springer 1976 · Zbl 0318.33004
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