论文标题
在素数之间的平方距离上
On the mean square gap between primes
论文作者
论文摘要
我们证明，对于任何固定的$ \ varepsilon> 0 $，我们的连续素数之间的平均差异平均大小为$ o（x^{0.23+ \ varepsilon}）$。这取决于Peck的结果，Peck给出了$ O（x^{0.25+ \ varepsilon}）$，以取代$ o（x^{0.23+ \ varepsilon}）$。关键成分是Harman的筛子，Heath-Brown的平均值定理，用于稀疏的Dirichlet多项式和Heath-Brown的$ r^*$结合。
We prove that the average size of the squares of differences between consecutive primes less than $x$ is $O(x^{0.23+\varepsilon})$ for any fixed $\varepsilon>0$. This improves on a result of Peck, who gave bound $O(x^{0.25+\varepsilon})$ in the place of $O(x^{0.23+\varepsilon})$. Key ingredients are Harman's sieve, Heath-Brown's mean value theorem for sparse Dirichlet polynomials and Heath-Brown's $R^*$ bound.
