非算术双曲共轭轨道的尖密度和可通约性。

IF 0.6 3区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Discrete & Computational Geometry Pub Date : 2023-01-01 DOI:10.1007/s00454-022-00455-z

Edoardo Dotti, Simon T Drewitz, Ruth Kellerhals

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引用次数: 0

摘要

对于非等差1尖双曲Coxeter 3-轨道的三个不同无限族(R m)， (S m)和(T m)，我们证明了属于同一序列的一对元素X k和Y l以及属于两个不同序列的大多数元素对的不可通约性。我们首先通过Vinberg空间和Vinberg形式来研究这个问题，Vinberg形式是一个与每个相应的基本Coxeter棱镜群相关的二次空间，它允许我们推断出一些部分结果。完整的证明是基于另一个可通约性不变量的解析行为。它由尖密度给出，并证明和利用了它的严格单调性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Cusp Density and Commensurability of Non-arithmetic Hyperbolic Coxeter Orbifolds.

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Cusp Density and Commensurability of Non-arithmetic Hyperbolic Coxeter Orbifolds.

For three distinct infinite families $(R_{m})$ , $(S_{m})$ , and $(T_{m})$ of non-arithmetic 1-cusped hyperbolic Coxeter 3-orbifolds, we prove incommensurability for a pair of elements $X_{k}$ and $Y_{l}$ belonging to the same sequence and for most pairs belonging two different ones. We investigate this problem first by means of the Vinberg space and the Vinberg form, a quadratic space associated to each of the corresponding fundamental Coxeter prism groups, which allows us to deduce some partial results. The complete proof is based on the analytic behavior of another commensurability invariant. It is given by the cusp density, and we prove and exploit its strict monotonicity.

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来源期刊

Discrete & Computational Geometry 数学-计算机：理论方法

CiteScore

1.80

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Discrete & Computational Geometry (DCG) is an international journal of mathematics and computer science, covering a broad range of topics in which geometry plays a fundamental role. It publishes papers on such topics as configurations and arrangements, spatial subdivision, packing, covering, and tiling, geometric complexity, polytopes, point location, geometric probability, geometric range searching, combinatorial and computational topology, probabilistic techniques in computational geometry, geometric graphs, geometry of numbers, and motion planning.