The asymptotic distribution of lattice points belonging to given residue classes on hyperboloids of special form

Under the assumption of a nontrivial shift of the zeros of Dirichlet $L$-series with quadratic character, asymptotic formulas are obtained for the number of lattice points in arbitrary regions on the hyperboloid $n=A\mathbf b^2+\mathbf{ac}$ belonging to given residue classes. A method for applying the results to the study of the distribution of lattice points on general second-order surfaces is outlined.
Bibliography: 19 titles.