Diophantine inequalities involving a prime and an almost-prime

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• 作者：Liyang Yang ^{yly12@mails.tsinghua.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Diophantine inequalities ; Sieve method ; Almost-primes
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：170
• 期：Complete
• 页码：347-367
• 全文大小：357 K

文摘

We prove that there are infinitely many solutions of where 839e52661c0a390bac5e7fb5eb2a3" title="Click to view the MathML source">λ₀${\lambda }_0$ is an arbitrary real number and 8cd6bc9adc95747cac9ac753" title="Click to view the MathML source">λ₁,λ₂∈R${\lambda }_1,{\lambda }_2\in \mathbb{R}$ with e7ecb67ec99951ec8c2c32" title="Click to view the MathML source">λ₂≠0${\lambda }_2\ne 0$ and e50cd12f91dca34d8627869aac1">$0>\frac{{\lambda }_1}{{\lambda }_2}$ not in 909c345694b25f075c576" title="Click to view the MathML source">Q$\mathbb{Q}$. This improves a result by Harman.