Critical Zeros and Unconditional Mean Value Theorems for twisted $PGL(2)$ and $PGL(3)$ $\mathrm{L}$-functions

Brian Conrey, Chung-Hang Kwan, Yongxiao Lin +1

Let ${\Pi }_0$ be a cuspidal automorphic representation of ${\mathrm{PGL}}_3({\mathbb{A}}_{\mathbb{Q}})$. In this paper, we use Levinson's method to prove that, as $Q\to \infty$, at lea…