International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1979 / Article

Open Access

Volume 2 |Article ID 635749 | https://doi.org/10.1155/S0161171279000089

D. G. Hazlewood, "Gaussian integers with small prime factors", International Journal of Mathematics and Mathematical Sciences, vol. 2, Article ID 635749, 10 pages, 1979. https://doi.org/10.1155/S0161171279000089

Gaussian integers with small prime factors

Received18 Apr 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.

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.


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