Abstract
Fifteen years ago Bost and Connes constructed a C*-dynamical system with the Calois group G(Qab /Q) as symmetry group and with phase transition related to properties of L-functions. Since then there have been numerous, and only partially succesful, attempts to generalize the system to arbitrary number fields. A few years ago, in order to extend that construction to imaginary quadratic feilds, Connes and Marcolli constructed a GL2-system, an analogue of the BC-system with Q* replaced by GL2(Q). They classified the KMSβ-states of the system for β > 2. Later Laca, Larsen and Neshveyev classified the KMSβ-states for all β ≠ 0, 1.