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Fractional Parts Of Non-Integer Powers Of Primes. II
Quarterly Journal of Mathematics ( IF 0.7 ) Pub Date : 2021-06-09 , DOI: 10.1093/qmath/haab031
Andrei Shubin 1
Affiliation  

We continue to study the distribution of prime numbers p, satisfying the condition $\{p^{\alpha} \} \in I \subset [0; 1)$, in arithmetic progressions. In this paper, we prove an analogue of Bombieri–Vinogradov theorem for 0 < α < 1/9 with the level of distribution $\theta = 2/5 - (3/5) \alpha$, which improves the previous result corresponding to $\theta \leqslant 1/3$.

中文翻译:

素数的非整数幂的小数部分。二

我们继续研究素数p的分布,满足条件$\{p^{\alpha} \} \in I \subset [0; 1)$,算术级数。在本文中,我们证明了 Bombieri-Vinogradov 定理的一个类似物,用于 0 < α<1/9,分布水平 $\theta = 2/5 - (3/5) \alpha$,这改进了之前对应于 $\theta \leqslant 1/3$ 的结果。
更新日期:2021-06-09
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