The ternary Goldbach problem with primes in positive density sets

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• 作者：Quanli Shen ^{qlshen@outlook.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：The ternary Goldbach problem ; Positive density ; Transference principle
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：168
• 期：Complete
• 页码：334-345
• 全文大小：288 K

文摘

Let a8e21a39657b844af6aba259342b966e" title="Click to view the MathML source">P$\mathcal{P}$ denote the set of all primes. P₁,P₂,P₃$P_1,P_2,P_3$ are three subsets of a8e21a39657b844af6aba259342b966e" title="Click to view the MathML source">P$\mathcal{P}$. Let $\underset{\_}{\delta }(P_i)$(i=1,2,3)$(i=1,2,3)$ denote the lower density of P_i$P_i$ in a8e21a39657b844af6aba259342b966e" title="Click to view the MathML source">P$\mathcal{P}$, respectively. It is proved that if $\underset{\_}{\delta }(P_1)>5/8$, $\underset{\_}{\delta }(P_2)\ge 5/8$, and $\underset{\_}{\delta }(P_3)\ge 5/8$, then for every sufficiently large odd integer n  , there exist p_i∈P_i$p_i\in P_i$ such that n=p₁+p₂+p₃$n=p_1+p_2+p_3$. The condition is the best possible.