Distribution of αp2 Modulo One with Prime Variable p of a Special Form
Let Pr denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, it is proved that, for α∈ℝ/ℚ, β∈ℝ, and 0<θ<10/1561, there exist infinitely many primes p, such that αp2+β<p−θ and p+2=P4, which constitutes an improvement upon the previous result....
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5516049 |
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| _version_ | 1832550816514310144 |
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| author | Fei Xue Jinjiang Li Min Zhang |
| author_facet | Fei Xue Jinjiang Li Min Zhang |
| author_sort | Fei Xue |
| collection | DOAJ |
| description | Let Pr denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, it is proved that, for α∈ℝ/ℚ, β∈ℝ, and 0<θ<10/1561, there exist infinitely many primes p, such that αp2+β<p−θ and p+2=P4, which constitutes an improvement upon the previous result. |
| format | Article |
| id | doaj-art-17b1d3d0bda54fe7a7b47cf383db0c8f |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-17b1d3d0bda54fe7a7b47cf383db0c8f2025-02-03T06:05:45ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55160495516049Distribution of αp2 Modulo One with Prime Variable p of a Special FormFei Xue0Jinjiang Li1Min Zhang2Department of Mathematics, China University of Mining and Technology, Beijing 100083, ChinaDepartment of Mathematics, China University of Mining and Technology, Beijing 100083, ChinaSchool of Applied Science, Beijing Information Science and Technology University, Beijing 100192, ChinaLet Pr denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, it is proved that, for α∈ℝ/ℚ, β∈ℝ, and 0<θ<10/1561, there exist infinitely many primes p, such that αp2+β<p−θ and p+2=P4, which constitutes an improvement upon the previous result.http://dx.doi.org/10.1155/2021/5516049 |
| spellingShingle | Fei Xue Jinjiang Li Min Zhang Distribution of αp2 Modulo One with Prime Variable p of a Special Form Journal of Mathematics |
| title | Distribution of αp2 Modulo One with Prime Variable p of a Special Form |
| title_full | Distribution of αp2 Modulo One with Prime Variable p of a Special Form |
| title_fullStr | Distribution of αp2 Modulo One with Prime Variable p of a Special Form |
| title_full_unstemmed | Distribution of αp2 Modulo One with Prime Variable p of a Special Form |
| title_short | Distribution of αp2 Modulo One with Prime Variable p of a Special Form |
| title_sort | distribution of αp2 modulo one with prime variable p of a special form |
| url | http://dx.doi.org/10.1155/2021/5516049 |
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