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BIMSA-YMSC Tsinghua Number Theory Seminar
BIMSA-YMSC Tsinghua Number Theory Seminar
Distributions of integral points and Zeta values
Distributions of integral points and Zeta values
Organizers
Hansheng Diao
, Heng Du
, Yueke Hu
, Bin Xu
, Yihang Zhu
Speaker
Li Cai
Time
Monday, April 27, 2026 10:00 AM - 11:00 AM
Venue
Shuangqing-B654
Abstract
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.