Academic Report of School of Mathematical Sciences [2026] No. 077

(Series Report for High-Level University Construction No. 1336)

Title：Comparing Hecke eigenvalues of automorphic representations for GL(2)

Speaker：Jianming Zeng (University of British Columbia)

Time：14:00-15:00, July 15, 2026

Location：Room 2433, Huiwen Building, Yuehai Campus, Shenzhen University

Abstract: We will talk about a variant of the strong multiplicity one theorem. Let $\pi_1$ and $\pi_2$ be two unitary cuspidal automorphic representations for GL(2) that are not twist-equivalent. We find a lower bound for the lower Dirichlet density of the set of places for which $|a_{v}(\pi_{1})|>|a_{v}(\pi_{2})|$, where $a_{v}(\pi_{i})$ is the trace of Langlands conjugacy class of $\pi_i$ at $v$.

Speaker Profile：Jianming Zeng is a Ph.D. candidate in the Department of Mathematics at the University of British Columbia in Canada, where his research focuses on number theory.

Faculty and students are welcome to attend!

Invited by: Yingnan Wang

School of Mathematical Sciences

July 10, 2026