| 关于两个素数和一个素数k次幂的丢番图不等式 |
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| 引用本文： | 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(中文版),2019,40(4):365-376. |
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| 作者姓名： | 朱立 |
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| 作者单位： | 同济大学数学科学学院, 上海 200092. |
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| 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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| 摘 要： | 令■设λ_1,λ_2,λ_3是不全同号的非零实数,且满足λ_1/λ_2为无理数,则对于任意实数η和ε 0,不等式■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.
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| 关 键 词： | Prime Davenport-Heilbronn method Diophantine inequalities |
| 收稿时间： | 2018/6/4 0:00:00 |
A Diophantine Inequality with Two Primes and One k-th Power of a Prime |
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| ZHU Li.A Diophantine Inequality with Two Primes and One k-th Power of a Prime[J].Chinese Annals of Mathematics,2019,40(4):365-376. |
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| Authors: | ZHU Li |
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| Institution: | School of Mathematical Science, Tongji University, Shanghai 200092, China. |
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| Abstract: | 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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| Keywords: | Prime Davenport-Heilbronn method Diophantine inequalities |
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