论文标题
关于与$ r_3（n）$的分布相关的差异
On a variance associated with the distribution of $r_3(n)$ in arithmetic progressions
论文作者
论文摘要
分析数理论中有两个问题在这些年来引起了很多关注。第一个是关于与算术进程中实序分布相关的方差的渐近公式，该方差起源于芭芭坦的工作。第二个是关于$ r_3（n）$的功能，三个正立方体总和的有序表示的数量，罗伯特·C·沃恩（Robert C. Vaughan）最近证明了几个结果。本文与这些问题的结合有关，应用了Hardy-Littlewood方法和Farey序列。
There are two questions in analytic number theory which have attracted much attention over the years. The first one is about the asymptotic formula for the variance associated with the distribution of a real sequence in arithmetic progressions, which origins in the work of Barban. The second one is about the function $r_3(n)$, the number of ordered representation of $n$ in the sum of three positive cubes, and several results are recently proved by Robert C. Vaughan. The paper is concerned with the conjunction of these questions, with the application of the Hardy-Littlewood Method and the Farey sequence.
