Nagoya Mathematical Journal

On generalized Whittaker functions on Siegel's upper half space of degree $2$

S. Niwa

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Nagoya Math. J., Volume 121 (1991), 171-184.

First available in Project Euclid: 14 June 2005

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Primary: 11F60: Hecke-Petersson operators, differential operators (several variables)
Secondary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05} 33C15: Confluent hypergeometric functions, Whittaker functions, $_1F_1$


Niwa, S. On generalized Whittaker functions on Siegel's upper half space of degree $2$. Nagoya Math. J. 121 (1991), 171--184.

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  • [1] M. Eichler, Quadratische Formen und orthogonale Groupen, Springer.
  • [2] S. Friedberg, Differential operators and theta series, Trans. Amer. Math. Soc, 287 (1985), 569-589.
  • [3] G.Kaufhold, Dirichletsche Reihe mitFunktionalgleichung in derTheorieder Modulfunktion 2. Grades, Math. Ann., 137 (1959), 454-476.
  • [4] M. Koecher, ber Thetareihen indefiniter quadratischer Formen, Math. Nachr., 9 (1953), 51-85.
  • [5] H. Maass, Die Differentialgleichungen in der Theorie der Siegelschen Modulfunk- tionen, Math. Ann., Bd., 126 (1953), 44-68.
  • [6] H. Maass, ber eine neue Art von nichtanalitischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Functionalgleichungen, Math. Ann., 121 (1949), 141-183.
  • [7] H. Maass, Dirichletsche Reihen und Modulfunktionen zweiten Grades, Acta Arith., 24 (1973), 225-238.
  • [8] H. Maass, ber die raumliehe Verteilung der Punkte in Gittern mit indefiniter Metrik, Math. Ann., 138 (1959), 287-315.
  • [9] S. Nakajima, On invariant differential operators on bounded symmetric domains of type IV, Proc. Japan Acad., 58, Ser. A (1982), 235-238.
  • [10] S. Nakajima, Invariant differential operators on SO(2,q)/S0(2)XS0(q) (3), Master these.
  • [11] G. Shimura, Confluent hypergeometric functions on tube domains, Math. Ann., 265 (1982), 269-302.
  • [12] H. Yamashita, On Whittaker vectors for generalized Gelfand-Graev representa- tions of semisimple Lie groups, J. Math. Kyoto Univ., 26-2 (1986), 263-298.
  • [13] H. Yamashita, On Whittaker vectors for generalized Gelfand-Graev representations of semi- simple Lie groups, Proc. Japan Acad., 61, Ser. A (1985), 213-216.
  • [14] H. Yamashita, Finite multiplicity theorems for induced representations of semisimple Lie groups and their applications to generalized Gelfand-Graev representations, Proc. Japan Acad., 63, Ser. A (1987), 153-156.
  • [15] H. Yamashita, Multiplicity one theorems for generalized Gelfand-Graev representations of semisimple Lie groups and Whittaker models for the discrete series, Preprint.
  • [16] H. Yoshida, Siegel's modular forms and the arithmetic of quadratic forms, Invent. Math., 60 (1980), 193-248.
  • [17] H. Yoshida, On Siegel modular forms obtained from theta series, J. reine angew. Math., 352 (1984), 184-219. Nagoya City College of Child Education Owariasahi, 88 Japan