Distributions of integral points and Zeta values
组织者
刁晗生
, 杜衡
, 胡悦科
, Bin Xu
, Yihang Zhu
演讲者
蔡立
时间
2026年04月27日 10:00 至 11:00
地点
Shuangqing-B654
摘要
We study the distribution of integral matrices with a fixed characteristic polynomial. We determine the leading term of the distribution in terms of zeta functions of orders. The proof is based on an equi-distribution property of orbits, a reformulation of the distribution into orbital integrals via the strong approximation with Brauer-Manin obstruction and the Tate-Nakayama duality, endoscopic fundamental lemma, and a critical input that links orbital integrals to residues of zeta functions of orders. This is a joint work with Taiwang Deng.