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A Tangent Inequality Over Primes

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Ukrainian Mathematical Journal Aims and scope

We introduce a new Diophantine inequality with prime numbers. Let \(1<c<\frac{10}{9}.\) We show that, for any fixed θ > 1, every sufficiently large positive number N, and a small constant ε > 0, the tangent inequality

$$\left|{p}_{1}^{c} {\mathrm{tan}}^{\theta }\left(\mathrm{log}{p}_{1}\right)+{p}_{2}^{c} {\mathrm{tan}}^{\theta }\left(\mathrm{log}{p}_{2}\right)+{p}_{3}^{c} {\mathrm{tan}}^{\theta }\left(\mathrm{log}{p}_{3}\right)-N\right|<\varepsilon $$

has a solution in prime numbers p1, p2, and p3.

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Authors and Affiliations

  1. Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Sofia, Bulgaria

    S. I. Dimitrov

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  1. S. I. Dimitrov
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Correspondence to S. I. Dimitrov.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 7, pp. 904–919, July, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i7.7184.

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Dimitrov, S.I. A Tangent Inequality Over Primes. Ukr Math J 75, 1034–1051 (2023). https://doi.org/10.1007/s11253-023-02245-z

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  • DOI: https://doi.org/10.1007/s11253-023-02245-z

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