关于Farey分数之间的三分之一区间
On the Intervals of a Third between Farey Fractions
摘要：
近年来，Farey点之间的间距分布引起了人们的关注。发现法里序列的连续元件之间的间隙$γ_{j+1}-γ_j$产生作为$Q\to\infty$的限制性测量。数值计算表明，对于任何$d\ge 2$，间隙$γ_{j+d}-γ_j$也产生一个限制措施，其支持是由显着的拓扑特征区分。本文证明了$d=2$空间分布的存在性，并完整地刻画了测度的相应支撑.
英文摘要：
The spacing distribution between Farey points has drawn attention in recent years. It was found that the gaps $γ_{j+1}-γ_j$ between consecutive elements of the Farey sequence produce, as $Q\to\infty$, a limiting measure. Numerical computations suggest that for any $d\ge 2$, the gaps $γ_{j+d}-γ_j$ also produce a limiting measure whose support is distinguished by remarkable topological features. Here we prove the existence of the spacing distribution for $d=2$ and characterize completely the corresponding support of the measure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
