3 research outputs found
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 ϕ₀(u,v) = u² + Av² , A > 0, A ≡ 1, 2(mod 4) and
ϕ0(u,v) belongs to the one-class kind G₀ of the quadratic forms of
discriminant −4A
Divisor problem in special sets of Gaussian integers
Let and be fixed sets of gaussian integers. We denote by the number of representations of in form , where . We construct the asymptotical formula for summatory function in case, when lie in the arithmetic progression, is a fixed sector of complex plane,