$PSL(2,\mathbb{Z})$的最小化表示
Minimal Presentation of $PSL(2,\mathbb{Z})$ Using Continuant Matrices with Integer Coefficients
摘要：
在这篇文章中，我们的目标是找到一个矩阵$A \in PSL(2,\mathbb{Z})$在所谓的连续矩阵，这是最有名的连分数理论中的作用的最短表示。在arXiv：1811.01229的第7章中，Morier-Génoud和Ovsienko在连续矩阵的所有系数都为正的限制下研究了这个问题。现在，目标是确定允许所有整数系数的最短表示。为了确定这种最小表示，将引入一些特征变换。它也将被调查的条件下，这样一个最小的介绍成为独特的。这些结果也推广到$PSL(2,\mathbb{Z})$的共轭类上.如果您想联系作者或您有一些与这项工作有关的问题，请随时写电子邮件到christian.streib@online.de。
英文摘要：
In this article, the goal is to find the shortest presentation of a matrix $A \in PSL(2,\mathbb{Z})$ in terms of the so-called continuant matrices which are most known for their role in continued fraction theory. In chapter 7 of arXiv:1811.01229, Morier-Génoud and Ovsienko investigate this problem with the restriction that all coefficients of the continuant matrices are positive. Now, the goal is to determine the shortest presentation allowing all integer coefficients. To determine this minimal presentation, a few characteristic transformations will be introduced. It will also be investigated under which conditions such a minimal presentation becomes unique. The results are also generalized on conjugacy classes in $PSL(2,\mathbb{Z})$. If you wish to contact the author or you have some questions related to this work, feel free to write an email to christian.streib@online.de.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
