Ergodic properties of flows for classes of positive binary quadratic forms in Gauss genera

Further development and refinement of previous results of A. V. Malyshev and the author concerning so-called discrete ergodic method of Yu. V. Linnik. An “ergodic theorem” and “mixing theorem” for flows of positive binary quadratic forms is proven, those describe the asymptotic distribution of the coefficients of these forms on residue classes and on the corresponding surface.