Gaussian integers with small prime factors

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 al...

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Main Author:	D. G. Hazlewood
Format:	Article
Language:	English
Published:	Hindawi Limited 1979-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	Gaussian integers small prime factors.
Online Access:	http://dx.doi.org/10.1155/S0161171279000089

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spelling	doaj-83dd1dc6ea1a4cc0a715dc4d2a129abc2020-11-24T23:40:05ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251979-01-0121819010.1155/S0161171279000089Gaussian integers with small prime factorsD. G. Hazlewood0Department of Mathematics, Southwest Texas State University, San Marcos, Texas 78666, USALet 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.http://dx.doi.org/10.1155/S0161171279000089Gaussian integerssmall prime factors.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	D. G. Hazlewood
spellingShingle	D. G. Hazlewood Gaussian integers with small prime factors International Journal of Mathematics and Mathematical Sciences Gaussian integers small prime factors.
author_facet	D. G. Hazlewood
author_sort	D. G. Hazlewood
title	Gaussian integers with small prime factors
title_short	Gaussian integers with small prime factors
title_full	Gaussian integers with small prime factors
title_fullStr	Gaussian integers with small prime factors
title_full_unstemmed	Gaussian integers with small prime factors
title_sort	gaussian integers with small prime factors
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1979-01-01
description	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.
topic	Gaussian integers small prime factors.
url	http://dx.doi.org/10.1155/S0161171279000089
work_keys_str_mv	AT dghazlewood gaussianintegerswithsmallprimefactors
_version_	1725511030185918464

Gaussian integers with small prime factors

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