Fractional parts of non-integer powers of primes. II

2020/11/23 by Shubin, Andrei
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2011.11790

Abstract

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

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