Zieve关于Hurwitz问题猜想的约化：化为三个分支点情形
Reduction of Zieve's Conjecture on the Hurwitz problem to Three Branch Points
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中文总结 AI 辅助
本文证明Zieve关于Hurwitz问题的猜想可约化为三分支点情形，并由此蕴含素数度猜想，核心方法是建立Zieve容许数据与三元组可实现性之间的联系。
中文摘要 AI 辅助
M. E. Zieve猜想：当球面上的候选数据满足每个分支划分的各部分最大公约数为1且满足最小公倍数条件时，该数据是可实现的。我们证明此猜想可约化到其三分支点情形。更精确地说，若每个Zieve容许三元组可实现，则每个具有至少四个分支点的Zieve容许数据可实现。特别地，Zieve猜想蕴含由A. L. Edmonds、R. S. Kulkarni和R. E. Stong提出的素数度猜想。生成式AI披露：OpenAI的GPT-5.6 Sol和GPT-6 Astra在整个研究及本文准备过程中提供协助，包括探索约化策略、证明开发与检查、符号和术语一致性检查，以及手稿起草和修订。作者仔细审查了所有AI辅助材料，并对所有数学主张及最终文本承担全部责任。
英文摘要
M. E. Zieve conjectured that a candidate datum over the sphere is realizable whenever the gcd of the parts of every branch partition is one and it satisfies the lcm condition. We prove that this conjecture reduces to its three-branch-point case. More precisely, if every Zieve-admissible triple is realizable, then every Zieve-admissible datum with at least four branch points is realizable. In particular, Zieve's conjecture implies the prime-degree conjecture posed by A. L. Edmonds, R. S. Kulkarni and R. E. Stong. Generative-AI disclosure. OpenAI's GPT-5.6 Sol and GPT-6 Astra assisted throughout the research and preparation of this article, including the exploration of reduction strategies, proof development and checking, consistency checks on notation and terminology, and manuscript drafting and revision. The authors reviewed all AI-assisted material with careful scrutiny and take full responsibility for all mathematical claims and for the final text.
发表机构
- University of Science and Technology of China (USTC)（中国科学技术大学）
- National Engineering Laboratory for Brain-inspired Intelligence Technology and Applications, School of Information Science and Technology, USTC（中国科学技术大学信息科学与技术学院脑启发智能技术与应用国家工程实验室）
机构由 AI 辅助整理，请以论文原文为准。
