论文标题
关于Farey序列索引的分布
On the distribution of index of Farey Sequences
论文作者
论文摘要
在本文中，我们研究了Farey分数索引的分布，该索引是由Hall和Shiu首先引入和研究的。我们为Fairy分数的索引时刻提供了渐近公式，该索引由dirichlet字符扭曲的Farey分数，用$ \ Mathcal {b} $ - 免费分母。此外，我们重新考虑[ALVZ08]早些时候所做的无方案例，并为带有无方形分母的指数时刻获得新的结果。我们还研究了指数函数的较高水平相关性，该函数在两个级别的相关性上推广了早期已知结果。
In this article, we study the distribution of index of Farey fractions which was first introduced and studied by Hall and Shiu. We provide asymptotic formulas for moments of index of Farey fractions twisted by Dirichlet characters for Farey fractions with $\mathcal{B}$-free denominators. Additionally, we reconsider the squarefree case earlier done in [ALVZ08], and obtain new results for moments of indices with square-free denominators. We also study higher level correlations of the index function generalizing earlier known results on two level correlations.
