函数域的Zeta函数
Zeta functions for function fields
摘要：
我们引入新的非交换zeta函数的曲线定义在有限域。有两种类型，即，使用半稳定丛定义的纯非阿贝尔zeta，以及针对由（约化群，极大抛物子群）组成的对定义的群zeta。得到了合理性和函数方程等基本性质。此外，还对它们的零点和一致性进行了讨论。在这篇文章的结尾，我们用我们即将发表的关于“抛物线还原、稳定性和质量”的文章解释了为什么这些齐塔人在本质上是非阿贝尔的。构造和结果在我们关于'Counting Bundles' arXiv：1202.0869的论文中公布。
英文摘要：
We introduce new non-abelian zeta functions for curves defined over finite fields. There are two types, i.e., pure non-abelian zetas defined using semi-stable bundles, and group zetas defined for pairs consisting of (reductive group, maximal parabolic subgroup). Basic properties such as rationality and functional equation are obtained. Moreover, conjectures on their zeros and uniformity are given. We end this paper with an explanation on why these zetas are non-abelian in nature, using our up-coming works on 'parabolic reduction, stability and the mass'. The constructions and results were announced in our paper on 'Counting Bundles' arXiv:1202.0869.
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。
