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International Journal of Mathematics and Mathematical Sciences
Volume 2, Issue 1, Pages 81-90
http://dx.doi.org/10.1155/S0161171279000089

Gaussian integers with small prime factors

Department of Mathematics, Southwest Texas State University, San Marcos, Texas 78666, USA

Received 18 April 1978

Copyright © 1979 Hindawi Publishing Corporation. 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.

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.