Fractional parts of noninteger powers of primes. II
Abstract
We continue to study the distribution of prime numbers $p$, satisfying the condition $\{ p^{\alpha} \} \in I \subset [0; 1)$, in arithmetic progressions. In the paper, we prove an analogue of BombieriVinogradov theorem for $0 < \alpha < 1/9$ with the level of distribution $\theta = 2/5  (3/5) \alpha$, which improves the previous result corresponding to $\theta \leq 1/3$.
 Publication:

arXiv eprints
 Pub Date:
 November 2020
 DOI:
 10.48550/arXiv.2011.11790
 arXiv:
 arXiv:2011.11790
 Bibcode:
 2020arXiv201111790S
 Keywords:

 Mathematics  Number Theory
 EPrint:
 35 pages