Shimura, Goro Confluent hypergeometric functions on tube domains. (English) Zbl 0502.10013 Math. Ann. 260, 269-302 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 81 Documents MSC: 11F27 Theta series; Weil representation; theta correspondences 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods 33C05 Classical hypergeometric functions, \({}_2F_1\) 32N99 Automorphic functions Keywords:analytic continuation; generalized confluent hypergeometric functions; Whittaker functions; Fourier expansion; applications to Eisenstein series for arithmetic groups; tube domains Citations:Zbl 0050.045; Zbl 0412.10020 PDF BibTeX XML Cite \textit{G. Shimura}, Math. Ann. 260, 269--302 (1982; Zbl 0502.10013) Full Text: DOI EuDML Digital Library of Mathematical Functions: §35.6(ii) Properties ‣ §35.6 Confluent Hypergeometric Functions of Matrix Argument ‣ Properties ‣ Chapter 35 Functions of Matrix Argument 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) · Zbl 0155.05901 [3] Kaufhold, G.: Dirichletsche Reihe mit Funktionalgleichung in der Theorie der Modulfunktion 2. Grades. Math. Ann.137, 454-476 (1959) · Zbl 0086.06701 [4] Koecher, M.: Über Thetareihen indefiniter quadratischer Formen. Math. Nachr.9, 51-85 (1953) · Zbl 0050.04501 [5] Maass, H.: Siegel’s modular forms and Dirichlet series. Lecture Notes in Mathematics. Vol. 216. Berlin, Heidelberg, New York: Springer 1971 · Zbl 0224.10028 [6] Shimura, G.: On the holomorphy of certain Dirichlet series. Proc. London Math. Soc.31, 79-98 (1975) · Zbl 0311.10029 [7] Siegel, C.L.: Über die analytische Theorie der quadratischen Formen. Ann. Math.36, 527-606 (1935) · JFM 61.0140.01 [8] Siegel, C.L.: Über die Zetafunktionen indefiniter quadratischer Formen. Math. Z.43, 682-708 (1938) · Zbl 0018.20305 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.