Fractional parts of non-integer powers of primes

Abstract

Let $\alpha >0$ be any fixed non-integer, $I$ be any subinterval of $[0;1)$. In the paper, we prove an analogue of Bombieri-Vinogradov theorem for the set of primes $p$ satisfying the condition $\{p^{\alpha }\}\in I$. This strengthens the previous result of Gritsenko and Zinchenko.

21 pages. Published in Mathematical Notes. This is a slightly modified version