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.
Author NameAffiliationE-mail
ZHU Li School of Mathematical Science, Tongji University, Shanghai 200092, China. zhuli15@tongji.edu.cn 
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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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