Counting geodesics of given commutator length

IF 1.2 2区数学 Q1 MATHEMATICS

Forum of Mathematics Sigma Pub Date : 2023-12-15 DOI:10.1017/fms.2023.114

Viveka Erlandsson, Juan Souto

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引用次数: 0

Abstract

Let

$\Sigma $

be a closed hyperbolic surface. We study, for fixed g, the asymptotics of the number of those periodic geodesics in

$\Sigma $

having at most length L and which can be written as the product of g commutators. The basic idea is to reduce these results to being able to count critical realizations of trivalent graphs in

$\Sigma $

. In the appendix, we use the same strategy to give a proof of Huber’s geometric prime number theorem.

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给定换元长度的大地线计数

让 $\Sigma $ 是一个封闭的双曲面。对于固定的 g，我们研究在 $\Sigma $ 中最长为 L 的周期性大地线的数量的渐近性，这些大地线可以写成 g 换向器的乘积。其基本思想是将这些结果简化为能够计算 $\Sigma $ 中三价图的临界实现。在附录中，我们用同样的策略给出了胡贝尔几何素数定理的证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Forum of Mathematics Sigma Mathematics-Statistics and Probability

CiteScore

1.90

自引率

5.90%

发文量

审稿时长

40 weeks

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