  The embedding of a torus into an inner form of PGL(2) defines an adelic toric
period. A general version of Duke's theorem states that this period
equidistributes as the discriminant of the splitting field tends to infinity.
In this paper we consider a torus embedded diagonally into two distinct inner
forms of PGL(2). Assuming the Generalized Riemann Hypothesis (and some
additional technical assumptions), we show simultaneous equidistribution as the
discriminant tends to infinity, with an effective logarithmic rate. Our proof
is based on a probabilistic approach to estimating fractional moments of
L-functions twisted by extended class group characters.
