复连分数、Kleinian 群与尖点游历的极值理论
动力系统
2025-10-14 v2 数论
摘要
对于五个复二次整数的 Euclid 环中的每一个，我们考虑一种数字取自该环的复连分数算法。我们证明了对于每种算法，其最大数字服从 Fréchet 分布。我们利用这一结果求出了与上述二次整数环相关的 Bianchi 流形上尖点游历的极限分布。
引用
@article{arxiv.2401.00626,
title = {Complex continued fractions, Kleinian and extremal theory for cusp excursions},
author = {Alexander Baumgartner and Mark Pollicott},
journal= {arXiv preprint arXiv:2401.00626},
year = {2025}
}
备注
19 pages, 4 figures Fixed typos. Converted appendix to new section and improved presentation of proofs. Added Theorem 1.3 (an application to Diophantine Approximation) along with a proof in Subsection 6.3. Changed title to more accurately reflect contents of preprint