  In his paper from 1996 on quadratic forms Heath-Brown developed a version of
the 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, and
approximated this quantity by the integral of the weight function against a
measure on the quadric. The weight function is assumed to be
$C_0^\infty$-smooth and vanish near the singularity of the quadric. In our work
we allow the weight function to be finitely smooth, not vanish at the
singularity and have an explicit decay at infinity. The paper uses only
elementary results from the number theory and is available to readers without a
number-theoretical background.
