A functional equation related to generalized entropies and the modular group

Abstract

We solve a functional equation connected to the algebraic characterization of generalized information functions. In order to prove the symmetry of the solution, we are led to the study of two homographies that generate the modular group; the group acts on a related functional equation. This suggest a more general relation between conditional probabilities and arithmetic.Mathematics Subject Classification (2010). Primary 97I70, 94A17 .