给定换元长度的大地线计数

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

摘要

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。

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Counting geodesics of given commutator length

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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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

期刊介绍： Forum of Mathematics, Sigma is the open access alternative to the leading specialist mathematics journals. Editorial decisions are made by dedicated clusters of editors concentrated in the following areas: foundations of mathematics, discrete mathematics, algebra, number theory, algebraic and complex geometry, differential geometry and geometric analysis, topology, analysis, probability, differential equations, computational mathematics, applied analysis, mathematical physics, and theoretical computer science. This classification exists to aid the peer review process. Contributions which do not neatly fit within these categories are still welcome. Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas will be welcomed. All published papers will be free online to readers in perpetuity.

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