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...
Gespeichert in:
| Datum: | 2023 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2023
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7184 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: | |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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: | 10.37863/umzh.v75i7.7184 |