Determination of $GL(3)$ Hecke-Maass forms from twisted central values

Abstract

Suppose ${\pi }_1$ and ${\pi }_2$ are two Hecke-Maass cusp forms for $SL(3,\mathbb{Z})$ such that for all primitive character $\chi$ we have $$L(\frac{1}{2},{\pi }_1\otimes \chi )=L(\frac{1}{2},{\pi }_2\otimes \chi ).$$ Then we show that ${\pi }_1={\pi }_2$.

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