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arXiv · 2408.01314

Diophantine Approximation with Piatetski-Shapiro Primes

Stephan Baier·Habibur Rahaman
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Abstract

We prove that for every irrational number $\alpha$, real number $\beta$, real number $c$ satisfying $1<c<9/8$ and positive real number $\theta$ satisfying $\theta<(9/c-8)/10$, there exist infinitely many primes of the form $p=\left[n^c\right]$ with $n\in \mathbb{N}$ such that $||\alpha p||<p^{-\theta}$.

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Stephan Baier, Habibur Rahaman. 2024-08-02. Diophantine Approximation with Piatetski-Shapiro Primes. https://arxiv.org/abs/2408.01314

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