International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 1, Pages 81-90

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

Copyright © 1979 D. G. Hazlewood. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.