  In his paper from 1996 on quadratic forms Heath-Brown developed a version of
circle method to count points in the intersection of an unbounded quadric with
a lattice of short period, if each point is given a weight. The weight function
is assumed to be $C_0^\infty$-smooth and to vanish near the singularity of the
quadric. In out work we allow the weight function to be finitely smooth and not
vanish near the singularity, and we give also an explicit dependence on the
weight function.
