Fractional parts of non-integer powers of primes

Andrei Shubin

Fractional parts of non-integer powers of primes

Number Theory 2020-10-30 v1

Authors: Andrei Shubin

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.

Keywords

fractional parts non-integer powers primes bombieri-vinogradov theorem distribution modulo 1

Cite

@article{arxiv.2010.15216,
  title  = {Fractional parts of non-integer powers of primes},
  author = {Andrei Shubin},
  journal= {arXiv preprint arXiv:2010.15216},
  year   = {2020}
}

Comments

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

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