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=b²–ac (D0). As a corollary one obtains the asymptotic behavior of the number of reduced indefinite binary quadratic forms of discriminant 4D.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 26–40, 1981.