报告人：马蔷

题目：The Kuznetsov formula for the Picard modular group $\mathrm｛SU｝(2,1;\ZZ[i])$

摘要：This talk explains the Kuznetsov formula from the viewpoint of relative trace formulas, beginning with the classical \mathrm{GL}(2) case. We then turn to the Picard modular group $\mathrm｛SU｝(2,1;\ZZ[i])$. A distinctive feature of this group is that the unipotent radical of the cusp is a Heisenberg group, so the Fourier expansion of an automorphic form decomposes according to the characters of its center; we treat the trivial-central-character coefficients. By constructing suitable Poincaré series and unfolding their inner products, we obtain a Kuznetsov formula whose geometric side involves explicit \mathrm{SU}(2,1) Kloosterman sums. We then give applications: a spectral large sieve inequality, a second moment bound for standard L-functions, and a weighted local Weyl law. This is joint work with Zhi Qi.

个人简介：Qiang Ma received her Ph.D. from Shandong University in 2023. From 2023 to 2025, she was a postdoctoral researcher at the Institute for Advanced Study in Mathematics, Zhejiang University. Since 2025, she has been a postdoctoral researcher at the Yau Mathematical Sciences Center, Tsinghua University. Her research interests lie in analytic number theory and automorphic forms.

邀请人：王志伟 122cc太阳集成游戏教授

报告时间：2026年7月10日 09:40-10:40

报告地点：知新楼B1044