Diophantine approximation by Piatetski-Shapiro primes

S. I. Dimitrov

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arXiv · 2006.01003

Diophantine approximation by Piatetski-Shapiro primes

S. I. Dimitrov

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Abstract

Let $[\,\cdot\,]$ be the floor function. In this paper we show that whenever $\eta$ is real, the constants $\lambda_i$ satisfy some necessary conditions, then for any fixed $1<c<38/37$ there exist infinitely many prime triples $p_1,\, p_2,\, p_3$ satisfying the inequality \begin{equation*} |\lambda_1p_1 + \lambda_2p_2 + \lambda_3p_3+\eta|<(\max p_j)^{{\frac{37c-38}{26c}}}(\log\max p_j)^{10} \end{equation*} and such that $p_i=[n_i^c]$, $i=1,\,2,\,3$.

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S. I. Dimitrov. 2020-06-01. Diophantine approximation by Piatetski-Shapiro primes. https://arxiv.org/abs/2006.01003

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