Hiroshima Mathematical Journal

The convergence of the Poincaré series on the limit set of a discrete group in several dimensions

Hisayasu Kurata

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 17, Number 1 (1987), 169-174.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206130197

Digital Object Identifier
doi:10.32917/hmj/1206130197

Mathematical Reviews number (MathSciNet)
MR886990

Zentralblatt MATH identifier
0627.30040

Subjects
Primary: 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]
Secondary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 30F40: Kleinian groups [See also 20H10]

Citation

Kurata, Hisayasu. The convergence of the Poincaré series on the limit set of a discrete group in several dimensions. Hiroshima Math. J. 17 (1987), no. 1, 169--174. doi:10.32917/hmj/1206130197. https://projecteuclid.org/euclid.hmj/1206130197


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References

  • [1] Ahlfors, L. V.: Mbius Transformations in Several Dimensions, Ordway Professorship Lectures in Math., Univ. of Minnesota, Minneapolis, 1981.
  • [2] Beardon, A. F.: The Geometry of Discrete Groups, Graduate Texts in Math. 91, Springer-Verlag, New York-Berlin, 1983.
  • [3] Frostman, O.: Sur les produits de Blaschke, Proc. Roy. Physiog. Soc. Lund, 12 (1942), 169-182.
  • [4] Nicholls, P. J.: Garnett points for Fuchsian groups, Bull. London Math. Soc., 12 (1980), 216-218.
  • [5] Pommerenke, Ch.: On the Green's function of Fuchsian groups, Ann. Acad. Sci. Fenn. Ser. AI Math., 2 (1976), 409-427.
  • [6] Sullivan, D.: On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, Ann. of Math. Stud., 97 (1981), 465-496.