Asymptotic distribution of integer-valued binary forms of a fixed discriminant

Under the assumption on the boundary of the zeros of the Dirichlet $L$-functions, one obtains a refinement of the results of Yu. V. Linnik and B. F. Skubenko on the uniformity of the distribution of integral points on the hyperboloids
$$ D=b^2-ac,\qquad(D\ne0). $$
As a corollary one obtains the asymptotic behavior of the number of reduced indefinite binary quadratic forms of discriminant $4D$.