有效映射类群动力学，I：Teichmüller空间中的格点计数

IF 2.3 1区数学 Q1 MATHEMATICS

Duke Mathematical Journal Pub Date : 2020-10-07 DOI:10.1215/00127094-2022-0066

Francisco Arana-Herrera

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引用次数: 5

摘要

我们证明了Teichm\ \ uller空间的映射类群轨道中位于给定中心和大半径的Teichm\ \ uller公制球内的点数的一个带有省电误差项的定量估计。对扇形和平分线计数也证明了同类估计。这些估计使Athreya, Bufetov, Eskin和Mirzakhani的渐近计数结果有效。

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Effective mapping class group dynamics, I: Counting lattice points in Teichmüller space

We prove a quantitative estimate with a power saving error term for the number of points in a mapping class group orbit of Teichm\"uller space that lie within a Teichm\"uller metric ball of given center and large radius. Estimates of the same kind are also proved for sector and bisector counts. These estimates effectivize asymptotic counting results of Athreya, Bufetov, Eskin, and Mirzakhani.

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来源期刊

Duke Mathematical Journal 数学-数学

CiteScore

3.40

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Information not localized