论文标题
几乎所有短时间间隔II几乎都是素数II
Almost primes in almost all short intervals II
论文作者
论文摘要
我们表明，对于几乎所有$ x $，间隔$（x，x，x+（\ log x）^{2.1}] $包含恰好有两个数量的产品。这在第二个作者的工作中有所改善，该作者的$ 3.51 $，以$ 2.1 $。获得了这一改进，我们在新的II估计中估算了一个新的Innerovation。
We show that, for almost all $x$, the interval $(x, x+(\log x)^{2.1}]$ contains products of exactly two primes. This improves on a work of the second author that had $3.51$ in place of $2.1$. To obtain this improvement, we prove a new type II estimate. One of the new innovations is to use Heath-Brown's mean value theorem for sparse Dirichlet polynomials.
