Inventiones mathematicae

, Volume 130, Issue 1, pp 159–188

Complete growth functions of hyperbolic groups

  • Rostislav Grigorchuk
  • Tatiana Nagnibeda

DOI: 10.1007/s002220050181

Cite this article as:
Grigorchuk, R. & Nagnibeda, T. Invent math (1997) 130: 159. doi:10.1007/s002220050181


. We study a generalization of the growth functions of finitely generated groups, namely the growth functions ΣgGgz|g| with coefficients in the group ring ℤ[G]. Rationality and methods of computation of such functions are discussed, in particular for hyperbolic groups. The complete growth functions of surface groups are explicitly computed. The operator and geodesic growth functions are also studied.

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Rostislav Grigorchuk
    • 1
  • Tatiana Nagnibeda
    • 2
  1. 1.Steklov Institute of Mathematics, Gubkina Str. 8, Moscow 117966, Russia (e-mail:,
  2. 2.Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, c.p. 240, 1211 Genève 24, Switzerland (e-mail: