Stability, Global Galois Representations and Non-Abelian Zeta Functions

在数学方面，有一些显著的进步：(1)我们引入了真正的非阿贝尔zeta函数，并研究了它们的基本性质；(2)深入研究了半稳定格，揭示了半稳定格与示踪公式Arthur截断的关系；(3)我们发现齐塔人理论与朗兰兹关于爱森斯坦系统的理论之间存在着天然的联系；(4)利用先进的Rankin-Selberg和Zagier方法，发现了与（约化群，极大抛物子群）s相关的阿贝尔ζ，从而揭示了对称性在黎曼假设中所起的隐藏作用；(5)在Tannakian范畴论的框架下，利用稳定性建立有限域上p进数域和函数域的一般（非阿贝尔）类场论。

In terms of mathematics, there are some remarkable advances : (1) We introduce genuine non-abelian zeta functions and study their basic properties ; (2) We intensively study semi-stable lattices and expose their relation with Arthur truncation of trace formula ; (3) We find a natural relation between our theory of zetas and Langlands' theory on Eisenstein systems ; (4) This then with an advanced Rankin-Selberg and Zagier method leads to the discovery of abelian zetas associated to (reductive group, maximal parabolic subgroup)s and hence an exposition of a hidden role played by symmetry in the Riemann Hypothesis ; (5) We initiate a program on using stability to establish a general (non-abelian) Class Field Theory for p-adic number fields and function fields over finite fields, under the framework of Tannakian category theory.