| 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,2013,34(5):599~608 |
| 4个素数平方及若干2的次幂和的丢番图逼近} |
| Diophantine Approximation with 4 Squares of Primes and Powers of 2 |
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| DOI： |
| 中文关键词: 丢番图不等式, 圆法, Goldbach型问题 |
| 英文关键词:Diophantine inequalities, Circle method, Goldbach-type problems |
| 基金项目:教育部博士点基金 (No.20120131120075) |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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