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Matematicheskie Zametki, 2020, Volume 108, Issue 3, paper published in the English version journal
(Mi mzm12883)
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This article is cited in 3 scientific papers (total in 3 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
Citation:
A. V. Shubin, “Fractional Parts of Noninteger Powers of Primes”, Math. Notes, 108:3 (2020), 394–408
Linking options:
https://www.mathnet.ru/eng/mzm12883
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