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arXiv · 2006.07069

Diophantine approximation with one prime of the form $p=x^2+y^2+1$

S. I. Dimitrov
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Abstract

Let $\varepsilon>0$ be a small constant. In the present paper we prove that whenever $\eta$ is real and constants $\lambda _i$ satisfy some necessary conditions, then 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|<\varepsilon \end{equation*} and such that $p_3=x^2 + y^2 +1$.

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S. I. Dimitrov. 2020-06-12. Diophantine approximation with one prime of the form $p=x^2+y^2+1$. https://arxiv.org/abs/2006.07069

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