Gaussian integers with small prime factors - D. G. Hazlewood (International Journal of Mathematics and Mathematical Sciences)
Let ψG(xt,x) denote the number of Gaussian integers with norm not exceeding x2t whose Gaussian prime factors have norm not exceeding x2. Previous estimates have required restrictions on the parameter t with respect to x. The purpose of this note is to present asymptotic estimates for ψG(xt,x) for all ranges of the parameter t with respect to x.