| 4个素数平方及若干2的次幂和的丢番图逼近} |
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| 引用本文： | 刘志新,孙海伟.4个素数平方及若干2的次幂和的丢番图逼近}[J].数学年刊A辑(中文版),2013,34(5):599-608. |
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| 作者姓名： | 刘志新 孙海伟 |
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| 作者单位： | 天津大学理学院数学系, 天津 300072.;山东大学(威海)数学与统计学院, 山东 威海 264209. |
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| 基金项目： | 教育部博士点基金 (No.20120131120075) |
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| 摘 要： | 证明了在一定条件下, 不等式
$|\lambda_1p_1^2+\lambda_2p_2^2+\lambda_3p_3^2+\lambda_4p_4^2+\mu_12^{m_1}+\cdots+\mu_s2^{m_s}+\varpi|<\eta$关
于素数$p_1, p_2, p_3, p_4$
和正整数$m_1, \cdots, m_s$有无穷多解, 改进了之前的结果.
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| 关 键 词： | 丢番图不等式 圆法 Goldbach型问题 |
Diophantine Approximation with 4 Squares of Primes and Powers of 2 |
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| LIU Zhixin and SUN Haiwei.Diophantine Approximation with 4 Squares of Primes and Powers of 2[J].Chinese Annals of Mathematics,2013,34(5):599-608. |
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| Authors: | LIU Zhixin and SUN Haiwei |
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| Institution: | Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China.;School of Mathematics and Statistics, Shandong University, Weihai 264209, Shandong, China. |
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| Abstract: | The authors prove that under certain conditions, the
inequality
$|\lambda_1p_1^2+\lambda_2p_2^2+\lambda_3p_3^2+\lambda_4p_4^2+\mu_12^{m_1}+\cdots+\mu_s2^{m_s}+\varpi|<\eta$
with primes $p_1, p_2, p_3, p_4$ and
positive integers $m_1, \cdots, m_s$ has infinitely many solutions.
This gives an improvement of the former results. |
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| Keywords: | Diophantine inequalities Circle method Goldbach-type problems |
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