论文标题
戈德巴赫（Goldbach）的出色设置几乎是双胞胎素数
The Exceptional Set in Goldbach's Problem with Almost Twin Primes
论文作者
论文摘要
我们考虑了二进制戈德巴赫问题中的出色设置，其中两个几乎是双胞胎素数的总和。我们的主要结果是在代表$ M = P_1+P_2 $的问题中为特殊设置提供了省电，其中$ P_1+2 $最多具有$ 2 $ PRIME DIVISOR，而$ P_2+2 $最多有$ 3 $ PRIME DIVISORS。证明中有三种主要成分：一种新的转移原理，例如筛的方法，结合了bombieri-friedlander-iwaniec和Maynard的分布估计水平，其中包括drappeau的想法，以产生节省动力，以及circle方法的概括蒙特哥马利和沃恩的参数。
We consider the exceptional set in the binary Goldbach problem for sums of two almost twin primes. Our main result is a power-saving bound for the exceptional set in the problem of representing $m=p_1+p_2$ where $p_1+2$ has at most $2$ prime divisors and $p_2+2$ has at most $3$ prime divisors. There are three main ingredients in the proof: a new transference principle like approach for sieves, a combination of the level of distribution estimates of Bombieri--Friedlander--Iwaniec and Maynard with ideas of Drappeau to produce power savings, and a generalisation of the circle method arguments of Montgomery and Vaughan that incorporates sieve weights.
