Determination of $\text{GL}(3)$ cusp forms by central values of quadratic twisted $L$-functions

Shenghao Hua, Bingrong Huang

Let $\varphi$ and ${\varphi }^{\prime }$ be two $\text{GL}(3)$ Hecke--Maass cusp forms. In this paper, we prove that $\varphi ={\varphi }^{\prime }\text{ or }\widetilde{{\varphi }^{\prime }}$ if there exists a nonzero constant $\kappa$ such that $$…