| 朱立.关于两个素数和一个素数 k 次幂的 丢番图不等式[J].数学年刊A辑,2019,40(4):365~376 |
| 关于两个素数和一个素数 k 次幂的 丢番图不等式 |
| A Diophantine Inequality with Two Primes and One k-th Power of a Prime |
| Received:June 04, 2018 |
| DOI：10.16205/j.cnki.cama.2019.0028 |
| 中文关键词: Prime, Davenport-Heilbronn method, Diophantine inequalities |
| 英文关键词:Prime, Davenport-Heilbronn method, Diophantine inequalities |
| 基金项目:本文受到国家自然科学基金(No.11771333)的资助. |
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| 中文摘要: |
| 令$\psi(k)= \left\{\!\!\!\begin{array}{ll}
\frac{1}{2k}-\frac{3}{10},\, &10$, 不等式
\begin{align*}
|\lambda_1p_1+\lambda_2p_2+\lambda_3p^k_3+\eta|\leq(\max\{p_1,p_2,p_3^k\}) ^{-\psi(k)+\varepsilon}
\end{align*}
有无穷多组素数解 $p_1,\,p_2,\,p_3$. 该结果改进了 Gambini, Languasco 和 Zaccagnini 的结果. |
| 英文摘要: |
| Let $\psi(k)= \left\{\!\!\!\begin{array}{ll}
\frac{1}{2k}-\frac{3}{10},\, &10 $, the inequality
\begin{align*}
|\lambda_1p_1+\lambda_2p_2+\lambda_3p^k_3+\eta|\leq(\max\{p_1,p_2,p_3^k\}) ^{-\psi(k)+\varepsilon}
\end{align*}
has infinitely many solutions in prime variables $p_1,\,p_2,\,p_3$.
This result constitutes an improvement on that of Gambini, Languasco and Zaccagnini. |
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