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arXiv · 2109.00536

Beatty primes from fractional powers of almost-primes

Victor Zhenyu Guo·Jinjiang Li·Min Zhang
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Abstract

Let $\alpha>1$ be irrational and of finite type, $\beta\in\mathbb{R}$. In this paper, it is proved that for $R\geqslant13$ and any fixed $c\in(1,c_R)$, there exist infinitely many primes in the intersection of Beatty sequence $\mathcal{B}_{\alpha,\beta}$ and $\lfloor n^c\rfloor$, where $c_R$ is an explicit constant depending on $R$ herein, $n$ is a natural number with at most $R$ prime factors, counted with multiplicity.

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Victor Zhenyu Guo, Jinjiang Li, Min Zhang. 2021-09-01. Beatty primes from fractional powers of almost-primes. https://arxiv.org/abs/2109.00536

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