Waring-Goldbach problem: Two squares and some higher powers

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• 作者：Yingjie Li^a ; Yingchun Cai^b ; ^{yingchuncai@mail.tongji.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11P32 ; 11N36
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：162
• 期：Complete
• 页码：116-136
• 全文大小：357 K

文摘

Let P_r$P_r$ denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper it is proved that for every large odd integer N  , and 5≤a≤8$5\le a\le 8$, a≤b$a\le b$, $\frac{13}{60}<\frac{1}{a}+\frac{1}{b}\le \frac{1}{3}$, the equation is solvable with x   being an almost-prime P_r(a,b)$P_{r(a,b)}$ and the other variables primes, where r(a,b)$r(a,b)$ is defined in the Theorem, in particular, r(6,7)=5$r(6,7)=5$. This result constitutes an refinement upon that of J. Brűdern.