International Journal of Mathematics and Mathematical Sciences 
Volume 2 (1979), Issue 1, Pages 81-90
doi:10.1155/S0161171279000089

Gaussian integers with small prime factors

D. G. Hazlewood

 Department of Mathematics, Southwest Texas State University, San Marcos 78666, Texas, USA
Received 18 April 1978

Abstract

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.