Complete growth functions of hyperbolic groups
- Cite this article as:
- Grigorchuk, R. & Nagnibeda, T. Invent math (1997) 130: 159. doi:10.1007/s002220050181
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. We study a generalization of the growth functions of finitely generated groups, namely the growth functions Σg∈Ggz|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.