ON PAIRS OF GOLDBACH-LINNIK EQUATIONS

被引：10

作者：

Kong, Yafang ^{[1
]}

Liu, Zhixin ^{[2
]}

机构：

[1] Chongqing Jiaotong Univ, Coll Math & Stat, Chongqing 400074, Peoples R China

[2] Tianjin Univ, Sch Sci, Dept Math, Tianjin 300072, Peoples R China

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2017年 / 95卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Goldbach-Linnik problem; circle method; pairs of equations; CONJECTURE; POWERS;

D O I：

10.1017/S000497271600071X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：199 / 208

页数：10

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