Piatetski-Shapiro primes in the intersection of multiple Beatty sequences

2021/09/01 by Guo, Victor Zhenyu, Li, Jinjiang, Zhang, Min
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2109.00461

Abstract

Suppose that α₁, α₂,β₁, β₂ ∈ℝ. Let α₁, α₂ > 1 be irrational and of finite type such that 1, α₁^-1, α₂^-1 are linearly independent over ℚ. Let c be a real number in the range 1 < c < 12/11. In this paper, it is proved that there exist infinitely many primes in the intersection of Beatty sequences B_α1,β1 = \lfloorα₁ n + β₁\rfloor, B_{α2, β2} = \lfloorα₂ n + β₂\rfloor and the Piatetski-Shapiro sequence \mathscrN^(c) = \lfloor n^c\rfloor. Moreover, we also give a sketch proof of Piatetski-Shapiro primes in the intersection of multiple Beatty sequences.

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