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On the vanishing of Poincaré series of rational functions
Author(s):
Irwin
Kra
Journal:
Bull. Amer. Math. Soc.
8
(1983),
63-66.
MSC (1980):
Primary 10D15, 30F40
MathSciNet review:
682823
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References:
- 1.
- L. V. Ahlfors, Finitely generated Kleinian groups, Amer. J. Math. 86 (1964), 413-429; 87 (1965), 759. MR 167618
- 2.
- L. Bers, Inequalities for finitely generated Kleinian groups, J. Analyse Math. 18 (1967), 23-41. MR 229817
- 3.
- L. Bers, Poincaré series for Kleinian groups, Comm. Pure Appl. Math. 26 (1973), 667-672; 27 (1974), 583. MR 333165
- 4.
- D. A. Hejhal, Monodromy groups and Poincaré series, Bull. Amer. Math. Soc. 84 (1978), 339-376. MR 492237
- 5.
- I. Kra, Automorphic forms and Kleinian groups, Benjamin, Reading, Mass., 1972. MR 357775
- 6.
- I. Kra, On the vanishing of and spanning sets for Poincaré series for cusp forms (to appear). MR 744999
- 7.
- I. Kra and B. Maskit, Bases for quadratic differentials, Comment. Math. Helv. (to appear). MR 694607
- 8.
- M. Nakada, Quasi-conformal stability of finitely generated function groups, Tôhoku Math. J. 30 (1978), 45-58. MR 470203
- 9.
- H. Petersson, Die linearen Relationen zwischen den ganzen Poincaréschen Reihen von reeller Dimension zur Modulgruppe, Abh. Math. Sem. Hamb. Univ. 12 (1938), 415-472.
- 10.
- H. Poincaré, Mémoire sur les fonctions fuchsiennes, Acta Math. 1 (1882), 193-294. MR 1554584
- 11.
- S. Wolpert, The Fenchel-Nielsen deformation, Ann. of Math. (2) 115 (1982), 501-528. MR 657237
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Additional Information:
DOI:
10.1090/S0273-0979-1983-15085-1
PII:
S 0273-0979(1983)15085-1
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