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The kernel of the Poincaré series operator

Author: Thomas A. Metzger
Journal: Proc. Amer. Math. Soc. 76 (1979), 289-292
MSC: Primary 30F35
MathSciNet review: 537090
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Abstract: By modifying a proof of Ljan, a natural basis for the kernel of the Poincaré series operator in the Bers space can be given. The basic idea behind the proof also extends to give such a basis in the case of a general Kleinian group and a discontinuous group acting on certain domains in $ {{\mathbf{C}}^n}$.

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  • [1] L. Bers, Completeness theorems for Poincaré series in one variable, Proc. of Internat. Sympos. on Linear Spaces (Jerusalem, 1960), Jerusalem Academic Press, Jerusalem, 1961, pp. 88-100. MR 0132829 (24:A2665)
  • [2] -, Automorphic forms and Poincaré series for infinitely generated Fuchsian groups, Amer. J. Math. 87 (1965), 196-214. MR 0174737 (30:4937)
  • [3] D. Drasin, Cusp forms and Poincaré series, Amer. J. Math. 90 (1968), 356-365. MR 0229818 (37:5384)
  • [4] C. J. Earle, Some remarks on Poincaré series, Compositio Math. 21 (1969), 167-176. MR 0249664 (40:2906)
  • [5] I. Kra, Automorphic forms and Kleinian groups, Benjamin, Reading, Mass., 1972. MR 0357775 (50:10242)
  • [6] G. M. Ljan, On the kernel of Poincaré's $ \theta $ operator, Soviet Math. Dokl. 17 (1976), 1283-1285.
  • [7] H. Petersson, Über Weierstrasspuntke und die expliziten Darstellung der automorphen Formen von reeler Dimension, Math. Z. 52 (1949), 32-59. MR 0033356 (11:428b)
  • [8] H. Poincaré, Mémoire sur les fonctions fuchsiennes, Acta Math. 1 (1882), 193-294. MR 1554584

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