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On boundedness of integrable automorphic forms in $ {\bf C}\sp{n}$


Author: Su Shing Chen
Journal: Proc. Amer. Math. Soc. 78 (1980), 342-344
MSC: Primary 32N10
DOI: https://doi.org/10.1090/S0002-9939-1980-0553372-9
MathSciNet review: 553372
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Abstract: We give a necessary and sufficient condition for an integrable automorphic form on a bounded symmetric domain D in $ {{\mathbf{C}}^n}$ to be bounded.


References [Enhancements On Off] (What's this?)

  • [1] C. J. Earle, A reproducing formula for integrable automorphic forms, Amer. J. Math 88 (1966), 867-870. MR 0206267 (34:6086)
  • [2] -, Some remarks on Poincaré series, Compositio Math. 21 (1969), 167-176. MR 0249664 (40:2906)
  • [3] R. C. Gunning and H. Rossi, Analytic functions of several complex variables, Prentice-Hall, Englewood Cliffs, N. J., 1965. MR 0180696 (31:4927)
  • [4] S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962. MR 0145455 (26:2986)
  • [5] J. Lehner, On the $ {A_q}(\Gamma ) \subset {B_q}(\Gamma )$ conjecture for infinitely generated groups, Discontinuous Groups and Riemann Surfaces (Proc. Conf. Univ. Maryland, College Park, Md., 1973), Ann. of Math. Studies, No. 79, Princeton Univ. Press, Princeton, N. J., 1974, pp. 283-288. MR 0357776 (50:10243)
  • [6] -, Automorphic forms, Discrete Groups and Automorphic Functions, Academic Press, New York, 1977, pp. 73-120. MR 0492234 (58:11380)
  • [7] T. A. Metzger and K. V. Rajeswara Rao, On integrable and bounded automorphic forms, Proc. Amer. Math. Soc. 28 (1971), 562-566. MR 0280713 (43:6432)
  • [8] D. Neibur and M. Sheingorn, Characterization of Fuchsian groups whose integrable forms are bounded, Ann. of Math. (2) 106 (1977), 239-258. MR 0466533 (57:6411)
  • [9] C. Pommerenke, On inclusion relations for spaces of automorphic forms, Advances in Complex Function Theory, Lecture Notes in Math., No. 505, Springer-Verlag, Berlin and New York, pp. 92-100. MR 0414862 (54:2954)
  • [10] A. Selberg, Automorphic functions and integral operators, Seminar on Analytic Functions, Institute for Advanced Study, Princeton, N. J., 1957, pp. 152-161.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0553372-9
Keywords: Automorphic form, bounded symmetric domain
Article copyright: © Copyright 1980 American Mathematical Society

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