2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140240We develop a general framework for analyzing KMS-states on C*-algebras arising from actions of Hecke pairs. We then specialize to the system recently introduced by Connes and Marcolli and classify its KMS-states for inverse temperatures β\ne 0,1. In particular, we show that for each β\in(1,2] there exists a unique KMS_β-state.23 pages; minor corrections, final versionOperator AlgebrasDynamical SystemsNumber Theorytext