  Expansive algebraic Z^d-actions corresponding to ideals are characterized by
the property that the complex variety of the ideal is disjoint from the
multiplicative unit torus. For such actions it is known that the limit for the
growth rate of periodic points exists and equals the entropy of the action. We
extend this result to actions for which the complex variety intersects the
multiplicative torus in a finite set. The main technical tool is the use of
homoclinic points which decay rapidly enough to be summable.
