| 史三英,巫朝霞.关于特殊形式素数$p$的$\alpha p^2$ 模$1$的分布[J].数学年刊A辑,2013,34(4):479~486 |
| 关于特殊形式素数$p$的$\alpha p^2$ 模$1$的分布 |
| On the Distribution of $\alpha p^2$ Modulo One \\ for Primes $p$ of a Special Type |
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| DOI： |
| 中文关键词: 殆素数, 线性筛法, 模1分布 |
| 英文关键词:Almost primes, Linear sieve, Distribution modulo one |
| 基金项目:国家自然科学基金(No.11071186, No.11201107)和安徽省自然科学基金(No.1208085QA01) |
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| 中文摘要: |
| 证明了如果$0<\theta < \frac {2}{375}$,
则对于无理数$\alpha$, 存在无限个素数$p$, 使得$p+2$不超过4个素因子, 并满足不等式$\|\alpha p^2+\beta\| |
| 英文摘要: |
| In this paper, it is proved that if $0<\theta < \frac {2}{375}$, then for any irrational $\alpha$,
there are infinitely many primes $p$ such that $p+2$ has at most four prime factors and $\|\alpha p^2+\beta\| |
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