Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2511.07146 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
Table des matières:
- Suppose that $c,d,α,β$ are real numbers satisfying the inequalities $1<d<c<79/71$ and $1<α<β<6^{1-d/c}$. In this paper, it is proved that, for sufficiently large real numbers $N_1$ and $N_2$ subject to $α\leqslant N_2/N_1^{d/c}\leqslantβ$, the following Diophantine inequalities system \begin{align*} \begin{cases} |p_1^c+p_2^c+p_3^c+p_4^c+p_5^c+p_6^c-N_1|<\varepsilon_1 (N_1) \\ |p_1^d+p_2^d+p_3^d+p_4^d+p_5^d+p_6^d-N_2|<\varepsilon_2 (N_2) \end{cases} \end{align*} is solvable in prime variables $p_1, p_2, p_3, p_4, p_5, p_6$, where \begin{align*} \begin{cases} \varepsilon_1 (N_1)=N_1^{-(1/c)(79/71-c)} (\log N_1)^{201}, \\ \varepsilon_2 (N_2)=N_2^{-(1/d)(79/71-d)} (\log N_2)^{201} . \end{cases} \end{align*} This result constitutes an improvement upon the previous result of Han-Liu-Zhang [5].