The exponent of convergence of Poincaré series

DOI10.1007/BF01540601zbMath0349.30012OpenAlexW1981249879MaRDI QIDQ1234777

Samuel James Patterson

Publication date: 1976

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/177788

Mathematics Subject Classification ID

Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (16)

Quasiconformal stability of Kleinian groups and an embedding of a space of flat conformal structures ⋮ The Laplacian for domains in hyperbolic space and limit sets of Kleinian groups ⋮ Limit sets of Kleinian groups and conformally flat Riemannian manifolds ⋮ On the critical exponent of infinitely generated Veech groups ⋮ Hausdorff dimension and Kleinian groups ⋮ The exponent of convergence of Poincaré series of combination groups ⋮ An alternative to wave mechanics on curved spaces ⋮ Remarks on Hausdorff dimensions for transient limits sets of Kleinian groups ⋮ Expanding graphs and invariant means ⋮ Positive harmonic functions on abelian covers ⋮ Further remarks on the exponent of convergence of Poincaré series ⋮ The divisor of Selberg's zeta function for Kleinian groups. Appendix A by Charles Epstein ⋮ On the spectrum of the Hecke groups ⋮ The Hausdorff dimension of limit sets of fuchsian groups of the type ( g;m) ⋮ On the Patterson-Sullivan measure of some discrete group of isometries ⋮ Kleinian groups with small limit sets

Cites Work

• The limit set of a Fuchsian group
• On boundaries of Teichmüller spaces and on Kleinian groups. I
• Inequalities for certain Fuchsian groups
• A lattice‐point problem in hyperbolic space
• The Exponent of Convergence of Poincaré Series
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