有限域上的算术-几何平均数列，其中 $q\equiv5\pmod{8}$
数论
2025-01-06 v2
摘要
算术-几何平均数列已在实数和复数上进行研究，最近，Michael J. Griffin、Ken Ono、Neelam Saikia 和 Wei-Lun Tsai 在满足 的有限域 上对其进行了考虑。在本文中，我们将算术-几何平均数列的定义推广到满足 的有限域 。我们解释了这些数列与图之间的联系，并展示了在 情况下相应图的性质。
引用
@article{arxiv.2501.00577,
title = {Arithmetic-geometric mean sequences over finite fields $\mathbb{F}_q$, where $q\equiv5\pmod{8}$},
author = {Natália Bátorová and Stevan Gajović},
journal= {arXiv preprint arXiv:2501.00577},
year = {2025}
}
备注
This paper is based on the bachelor thesis of the first author, cosupervised by the second author in the academic year 2023/2024 at Charles University in Prague. This version is more expository and slightly less formal than the version that will soon be published in the Bulletin of the Australian Mathematical Society