Igusa-Todorov functions for Artin algebras

In this paper we study the behavior of the Igusa-Todorov functions for Artin algebras A with finite injective dimension, and Gorenstein algebras as a particular case. We show that the ϕ-dimension and ψ-dimension are finite in both cases. Also we prove that monomial, gentle and cluster tilted algebras have finite ϕ-dimension and finite ψ-dimension.