This article is cited in 4 papers

Papers published in the English version of the journal

Fractional Parts of Noninteger Powers of Primes

A. V. Shubin

Moscow Institute of Physics and Technology, Dolgoprudny, 141701 Russia

Abstract: Let $\alpha > 0$ be any fixed noninteger. In the paper, we prove an analogue of the Bombieri–Vinogradov theorem for the set of primes $p$ satisfying the condition $\{ p^{\alpha} \} < 1/2$. This generalizes the previous result of Gritsenko and Zinchenko.

Keywords: prime numbers, arithmetic progressions, fractional parts, Bombieri–Vinogradov theorem, exponential sums.

Received: 30.04.2020

Language: English

 English version: Mathematical Notes, 2020, 108:3, 394–408

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