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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| Format: | Article |
| Language: | English |
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Wiley
1979-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171279000089 |
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| _version_ | 1832549313878687744 |
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| author | D. G. Hazlewood |
| author_facet | D. G. Hazlewood |
| author_sort | D. G. Hazlewood |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-83dd1dc6ea1a4cc0a715dc4d2a129abc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1979-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-83dd1dc6ea1a4cc0a715dc4d2a129abc2025-02-03T06:11:40ZengWileyInternational 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. |
| spellingShingle | D. G. Hazlewood Gaussian integers with small prime factors International Journal of Mathematics and Mathematical Sciences Gaussian integers small prime factors. |
| title | 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_short | Gaussian integers with small prime factors |
| title_sort | gaussian integers with small prime factors |
| topic | Gaussian integers small prime factors. |
| url | http://dx.doi.org/10.1155/S0161171279000089 |
| work_keys_str_mv | AT dghazlewood gaussianintegerswithsmallprimefactors |