In this talk we state (one of) the main conjectures of Darmon-Vonk, which says that the values of rigid meromorphic cocycles at RM points are algebraic, and generate ring class fields of real quadratic fields. In addition, they formulate a reciprocity law for these values which describes the action of the associated ring class group. We will discuss the computational evidence for this conjecture.

3.1-3.2 of Darmon-Vonk