论文标题
关于正方形，立方体和更高力量的Waring-Goldbach问题
On Waring-Goldbach Problem for Squares, Cubes and Higher Powers
论文作者
论文摘要
令$ \ Mathcal {p} _r $表示几乎可以用$ r $ prime因子，根据多重性计算。在本文中，我们将沃恩的结果推广为三元允许的指数。 Moreover, we use the refined admissible exponent to prove that, for $3\leqslant k\leqslant 14$ and for every sufficiently large even integer $n$, the following equation \begin{equation*} n=x^2+p_1^2+p_2^3+p_3^3+p_4^3+p_5^k \end{equation*} is solvable with $ x $是一个几乎主要的$ \ nathcal {p} _ {r（k）} $和其他变量素数，其中$ r（k）$在定理中定义。该结果构成了先前结果的加深。
Let $\mathcal{P}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, we generalize the result of Vaughan for ternary admissible exponent. Moreover, we use the refined admissible exponent to prove that, for $3\leqslant k\leqslant 14$ and for every sufficiently large even integer $n$, the following equation \begin{equation*} n=x^2+p_1^2+p_2^3+p_3^3+p_4^3+p_5^k \end{equation*} is solvable with $x$ being an almost-prime $\mathcal{P}_{r(k)}$ and the other variables primes, where $r(k)$ is defined in Theorem. This result constitutes a deepening upon that of previous results.
