标题： 双七边形的斜率间隙分布及确定胜利向量的算法 显示英文标题

标题： Slope gap distribution of the double heptagon and an algorithm for determining winning vectors

摘要： 在本文中，我们研究了翻译曲面上鞍连接斜率之间的归一化间隔的分布。 具体而言，我们描述了一种找到“获胜全纯向量”的方法，该方法由Kumanduri-Sanchez-Wang在arXiv:2102.10069中定义，这是计算任意Veech曲面的斜率间隔分布的关键步骤。 然后，我们将此方法应用于显式计算正双七边形翻译曲面的间隔分布。 这扩展了Athreya-Chaika-Lelievre在arXiv:1308.4203上关于“黄金L”翻译曲面的间隔分布的工作，该曲面等价于正双五边形曲面。 显示英文摘要

摘要： In this paper, we study the distribution of renormalized gaps between slopes of saddle connections on translation surfaces. Specifically, we describe a procedure for finding the "winning holonomy vectors" as defined by Kumanduri-Sanchez-Wang in arXiv:2102.10069, which constitutes a key step in calculating the slope gap distribution for an arbitrary Veech surface. We then apply this method to explicitly compute the gap distribution for the regular double heptagon translation surface. This extends work of Athreya-Chaika-Lelievre in arXiv:1308.4203 on the gap distribution for the "golden L" translation surface, which is equivalent to the regular double pentagon surface.