Kleinian groups with unbounded limit sets
Glasgow mathematical journal, Tome 13 (1972) no. 1, pp. 24-28
Voir la notice de l'article provenant de la source Cambridge University Press
The easiest way to construct automorphic functions is by means of the Poincaré series. If G is a Kleinian group with ∞ an ordinary point of G and if k ≧ 4, thenwhere Vz=(az+b)/(cz+d) and ad-bc=1. The convergence of this series is the crucial step in showing that the Poincaré series converges and is an automorphic form on G If ∞ is a limit point of ∞ the series in (1) may diverge and one can derive automorphic forms on ∞ from the Poincaré series of some conjugate group. These constructions are described in greater detail in /3, pp. 155–165].
Beardon, A. F. Kleinian groups with unbounded limit sets. Glasgow mathematical journal, Tome 13 (1972) no. 1, pp. 24-28. doi: 10.1017/S0017089500001324
@article{10_1017_S0017089500001324,
author = {Beardon, A. F.},
title = {Kleinian groups with unbounded limit sets},
journal = {Glasgow mathematical journal},
pages = {24--28},
year = {1972},
volume = {13},
number = {1},
doi = {10.1017/S0017089500001324},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500001324/}
}
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[3] 3.Lehner, J., Discontinuous groups and automorphic functions, Amer. Math. Soc. Math. Surveys, No 8 (Providence, R.I., 1964). Google Scholar | DOI
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