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Confluent hypergeometric functions on tube domains. (English) Zbl 0502.10013

MSC:
11F27Theta series; Weil representation; theta correspondences
22E45Analytic representations of Lie and linear algebraic groups over real fields
33C05Classical hypergeometric functions, 2 F 1
32N99Automorphic functions (several complex variables)
References:
[1]Indik, R.: Thesis, Princeton University 1982
[2]Jacquet, H.: Fonctions de Whittaker associées aux groupes de Chevalley. Bull. Soc. Math. France95, 243-309 (1967)
[3]Kaufhold, G.: Dirichletsche Reihe mit Funktionalgleichung in der Theorie der Modulfunktion 2. Grades. Math. Ann.137, 454-476 (1959) · Zbl 0086.06701 · doi:10.1007/BF01360845
[4]Koecher, M.: Über Thetareihen indefiniter quadratischer Formen. Math. Nachr.9, 51-85 (1953) · Zbl 0050.04501 · doi:10.1002/mana.19530090105
[5]Maass, H.: Siegel’s modular forms and Dirichlet series. Lecture Notes in Mathematics. Vol. 216. Berlin, Heidelberg, New York: Springer 1971
[6]Shimura, G.: On the holomorphy of certain Dirichlet series. Proc. London Math. Soc.31, 79-98 (1975) · Zbl 0311.10029 · doi:10.1112/plms/s3-31.1.79
[7]Siegel, C.L.: Über die analytische Theorie der quadratischen Formen. Ann. Math.36, 527-606 (1935) · doi:10.2307/1968644
[8]Siegel, C.L.: Über die Zetafunktionen indefiniter quadratischer Formen. Math. Z.43, 682-708 (1938) · doi:10.1007/BF01181113