Distribution of integral points on the determinant surface

One obtains an asymptotic formula with remainder term for the number of second-order integral matrices with an increasing determinant, belonging to a given region of the discriminant surface and to a given residue class. The results are more accurate than in A. M. Istamov's paper (this issue, pp. 14–17) and are obtained in a somewhat different manner. The presentation is more detailed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 93, pp. 30–40, 1980.