A tangent inequality over primes
UDC 511 We introduce a new Diophantine inequality with prime numbers. Let $1<c<\dfrac{10}{9}.$ We show that, for any fixed $\theta>1,$ every sufficiently large positive number $N,$ and a small constant $\varepsilon>0,$ the tangent inequality \begin{equatio...
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| Date: | 2023 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7184 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865793802429530112 |
|---|---|
| author | Dimitrov, S. I. Dimitrov, S. I. |
| author_facet | Dimitrov, S. I. Dimitrov, S. I. |
| author_institution_txt_mv | [
{
"author": "S. I. Dimitrov",
"institution": "Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Bulgaria"
}
] |
| author_sort | Dimitrov, S. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-08-15T15:57:32Z |
| description | UDC 511
We introduce a new Diophantine inequality with prime numbers. Let $1<c<\dfrac{10}{9}.$ We show that, for any fixed $\theta>1,$ every sufficiently large positive number $N,$ and a small constant $\varepsilon>0,$ the tangent inequality \begin{equation*} \big|p^c_1\tan^\theta(\log p_1)+ p^c_2\tan^\theta(\log p_2)+ p^c_3\tan^\theta(\log p_3) -N\big|<\varepsilon \end{equation*} has a solution in prime numbers $p_1,$ $p_2,$ and $p_3.$ |
| doi_str_mv | 10.37863/umzh.v75i7.7184 |
| first_indexed | 2026-03-24T03:31:45Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7184 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:31:45Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-71842023-08-15T15:57:32Z A tangent inequality over primes Dimitrov, S. I. Dimitrov, S. I. Diophantine inequality, Tangent inequality, Prime numbers UDC 511 We introduce a new Diophantine inequality with prime numbers. Let $1<c<\dfrac{10}{9}.$ We show that, for any fixed $\theta>1,$ every sufficiently large positive number $N,$ and a small constant $\varepsilon>0,$ the tangent inequality \begin{equation*} \big|p^c_1\tan^\theta(\log p_1)+ p^c_2\tan^\theta(\log p_2)+ p^c_3\tan^\theta(\log p_3) -N\big|<\varepsilon \end{equation*} has a solution in prime numbers $p_1,$ $p_2,$ and $p_3.$ УДК 511 Дотична нерівність над простими числами Введено нову діофантову нерівність з простими числами. Нехай $1<c<\dfrac{10}{9}.$ Показано, що для довільного фіксованого $\theta>1,$ кожного достатньо великого додатного числа $N$ та малого сталого числа $\varepsilon>0$  дотична нерівність \begin{equation*} \big|p^c_1\tan^\theta(\log p_1)+ p^c_2\tan^\theta(\log p_2)+ p^c_3\tan^\theta(\log p_3) -N\big|<\varepsilon \end{equation*} має розв'язок у простих числах $p_1,$ $p_2$ та $p_3.$  Institute of Mathematics, NAS of Ukraine 2023-07-25 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7184 10.37863/umzh.v75i7.7184 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 7 (2023); 904 - 919 Український математичний журнал; Том 75 № 7 (2023); 904 - 919 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7184/9753 Copyright (c) 2023 Stoyan Dimitrov |
| spellingShingle | Dimitrov, S. I. Dimitrov, S. I. A tangent inequality over primes |
| title | A tangent inequality over primes |
| title_full | A tangent inequality over primes |
| title_fullStr | A tangent inequality over primes |
| title_full_unstemmed | A tangent inequality over primes |
| title_short | A tangent inequality over primes |
| title_sort | tangent inequality over primes |
| topic_facet | Diophantine inequality Tangent inequality Prime numbers |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7184 |
| work_keys_str_mv | AT dimitrovsi atangentinequalityoverprimes AT dimitrovsi atangentinequalityoverprimes AT dimitrovsi tangentinequalityoverprimes AT dimitrovsi tangentinequalityoverprimes |