On the mean square of the Epstein zeta-function

Abstract

We consider the second power moment of the Epstein zeta-function and construct the asymptotic formula in special case, when \(\varphi_{0}(u,v)=u^{2}+Av^{2}\), \(A>0\), \(A\equiv1,2(mod\,4)\) and \(\varphi_{0}(u,v)\) belongs to the one-class kind \(G_{0}\) of the quadratic forms of discriminant \(-4A\).