Fractional parts of non-integer powers of primes. II

Andrei Shubin

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arXiv · 2011.11790

Fractional parts of non-integer powers of primes. II

Andrei Shubin

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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 $\theta \leq 1/3$.

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Andrei Shubin. 2020-11-23. Fractional parts of non-integer powers of primes. II. https://arxiv.org/abs/2011.11790

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