Fractional parts of non-integer 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 Bombieri-Vinogradov theorem for $0<\alpha <1/9$ with the level of distribution $\theta =2/5-(3/5)\alpha$, which improves the previous result corresponding to $\theta \le 1/3$.

35 pages