Affiliation:
1. Data Science Institute and School of Mathematics, Shandong University , Jinan, Shandong 250100, China
Abstract
Abstract
Let $\phi $ and $\phi ^{\prime}$ be two $\operatorname {GL}(3)$ Hecke–Maass cusp forms. In this paper, we prove that $\phi =\phi ^{\prime} \textrm {or }\widetilde {\phi ^{\prime}}$ if there exists a nonzero constant $\kappa $ such that $L(\frac {1}{2},\phi \otimes \chi _{8d})=\kappa L(\frac {1}{2},\phi ^{\prime}\otimes \chi _{8d})$ for all positive odd square-free positive $d$. Here, $\widetilde {\phi ^{\prime}}$ is dual form of $\phi ^{\prime}$ and $\chi _{8d}$ is the quadratic character $(\frac {8d}{\cdot })$. To prove this, we obtain asymptotic formulas for twisted 1st moment of central values of quadratic twisted $L$-functions on $\operatorname {GL}(3)$, which will have many other applications.
Funder
National Key R&D Program of China
NSFC
Young Taishan Scholars Program
Publisher
Oxford University Press (OUP)
Cited by
3 articles.
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