ON PAIRS OF GOLDBACH–LINNIK EQUATIONS
ON PAIRS OF GOLDBACH–LINNIK EQUATIONS
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DOI：
10.1017/s000497271600071x
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发表时间：
2016-10
影响因子：
0.7
通讯作者：
Yafang Kong;Zhixin Liu
中科院分区：
文献类型：
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作者：
Yafang Kong;Zhixin Liu
本文证明了任意一对大的正偶数都可以表示为一对Goldbach-Linnik方程，即两个素数的线性方程和两个素数的$k次方程组。特别地，一般而言，$k=34$2的幂就足够了，而在广义黎曼假设下，$k=18$。我们的结果加强了以前结果中的2的幂的个数，一般而言，它给出了$k=62$，在广义黎曼假设下，$k=31$。
In this paper, we show that every pair of large positive even integers can be represented in the form of a pair of Goldbach–Linnik equations, that is, linear equations in two primes and $k$ powers of two. In particular, $k=34$ powers of two suffice, in general, and $k=18$ under the generalised Riemann hypothesis. Our result sharpens the number of powers of two in previous results, which gave $k=62$ , in general, and $k=31$ under the generalised Riemann hypothesis.