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The exponent of convergence of poincaré series

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Abstract

This paper continues the systematic study of the exponent of convergence δ(G) of a Fuchsian groupG begun byA. F. Beardon. The object is to show that in various senses δ(G) is a continuous function ofG. In view of the incompleteness of our knowledge about δ(G) considerable attention is paid to illustrative examples.

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References

  1. Ahlfors, L.: Lectures on Quasiconformal Mappings. toronto-New York-London: Van Nostrand. 1966.

    Google Scholar 

  2. Bers, L.: Teichmüller spaces and Kleinian groups. Ann. of Math.91, 570–600 (1970).

    Google Scholar 

  3. Beardon, A. F.: The exponent of convergence of Poincaré series. Proc. London Math. Soc.18, 461–483 (1968).

    Google Scholar 

  4. Beardon, A. F.: Inequalities for certain Fuchsian groups. Acta Math.127, 221–258 (1971).

    Google Scholar 

  5. Elstrodt, J.: Die Resolvente zum Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. Math. Ann.203, 295–330 (1973); Math. Z.132, 99–134 (1973); Math. Ann.208, 99–132 (1974).

    Google Scholar 

  6. Kra, I.: Automorphic Forms and Kleinian Groups, Reading, Mass.: Benjamin. 1972.

    Google Scholar 

  7. Lehner, J.: Discontinuous Groups and Automorphic Functions. Providence: amer. Math. Soc. 1964.

    Google Scholar 

  8. Patterson, S. J.: The limit set of a Fuchsian group. Acta Math.136, 241–273 (1976).

    Google Scholar 

  9. Patterson, S. J.: The Laplacian operator on a Riemann Surface. Comp. Math.31, 83–107 (1975).

    Google Scholar 

  10. Patterson, S. J.: A lattice-point problem in hyperbolic space. Mathematika22, 81–88 (1975).

    Google Scholar 

  11. Selberg, A.: Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spacs with applications to Dirichlet series. J. Indian Math. Soc.20, 47–87 (1956).

    Google Scholar 

  12. Selberg, A.: On discontinuous groups in higher dimensional symmetric spaces. Contributions to Function Theory. Bombay. 1960, p. 147–164.

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Authors and Affiliations

  1. Mathematisches Institut der Universität, Bunsenstraße 3-5, D-3400, Göttingen, Federal Republic of Germany

    S. J. Patterson

  2. DPMMS, University of Cambridge, 16 Mill Lane, CB21SB, Cambridge, England

    S. J. Patterson

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  1. S. J. Patterson
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Patterson, S.J. The exponent of convergence of poincaré series. Monatshefte für Mathematik 82, 297–315 (1976). https://doi.org/10.1007/BF01540601

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  • DOI: https://doi.org/10.1007/BF01540601

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