负弯曲流形和树中法雷射线的联合局部等分布

Pub Date : 2024-01-08 DOI:10.1017/etds.2023.116

JOUNI PARKKONEN, FRÉDÉRIC PAULIN

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引用次数: 0

摘要

我们证明了在等分布等距超曲面上具有给定密度的共同垂线的联合局部等分布结果，其方向是支持在截断稳定叶上的度量。我们恢复了马克洛夫关于给定密度下法雷分数联合部分等分布的一个结果，并给出了几个类似的算术应用，包括在布鲁哈特-提茨树中的应用。

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Joint partial equidistribution of Farey rays in negatively curved manifolds and trees

We prove a joint partial equidistribution result for common perpendiculars with given density on equidistributing equidistant hypersurfaces, towards a measure supported on truncated stable leaves. We recover a result of Marklof on the joint partial equidistribution of Farey fractions at a given density, and give several analogous arithmetic applications, including in Bruhat–Tits trees.

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