  We study lattice points on hyperbolic circles centred at Heegner points of
class number one. Our main result is that, on a density one subset of radii
tending to infinity, the angles of such points equidistribute on the unit
circle. To prove this, we establish a connection between lattice points and
algebraic integers in the associated field having norm of a special form and
satisfying a congruence condition. As a by-product of this, we obtain an
explicit formulation of the classical hyperbolic circle problem as a shifted
convolution sum for the function that counts the number of algebraic integers
with given norm. Along the way, we also prove a lower bound for shifted
B-numbers, which is done by sieve methods.
