On the mean square of the Epstein zeta-function

We consider the second power moment of the Epstein zeta-function and construct the asymptotic formula in special case, when $\varphi_{0}(u,v)=u^{2}+Av^{2}$, $A>0$, $A\equiv 1,2(mod\,4)$ and $\varphi_{0}(u,v)$ belongs to the one-class kind $G_{0}$ of the quadratic forms of discriminant $-4A$.