论文标题
$ gl（3）\ times gl（2）$ $ L $ functions in $ gl（3）$频谱方面
Subconvexity for $GL(3)\times GL(2)$ $L$-functions in $GL(3)$ spectral aspect
论文作者
论文摘要
Let $f$ be a $SL(2,\mathbb{Z})$ holomorphic cusp form or the Eisenstien series $E(z,1/2)$ and $π$ be a $SL(3,\mathbb{Z})$ Hecke-Maass cusp form with its Langlands parameter $μ$ in generic position i.e. away from Weyl chamber walls and away from self dual forms.我们研究了一个放大的第二钟$ \ sum_ {j} a（π_j）| l（1/2，π_j\ times f）|^2 $，并推断出子范围bond \ begin \ begin {equation*} l（1/2，π\ times f）\ ll_ {f，ll_} \ end {equation*}作为推论，当$ f = e（z，1/2）$时，我们还获得了subconvexity bound \ begin {equation*} l（1/2，π）\ll_ε\ |μ\ |μ\ |^|^{3/4-1/4044+ε}。 \ end {equation*}
Let $f$ be a $SL(2,\mathbb{Z})$ holomorphic cusp form or the Eisenstien series $E(z,1/2)$ and $π$ be a $SL(3,\mathbb{Z})$ Hecke-Maass cusp form with its Langlands parameter $μ$ in generic position i.e. away from Weyl chamber walls and away from self dual forms. We study an amplified second moment $\sum_{j} A(π_j)|L(1/2,π_j\times f)|^2$ and deduce the subconvexity bound \begin{equation*} L(1/2,π\times f)\ll_{f,ε} \|μ\|^{3/2-1/2022+ε}. \end{equation*} As a corollary, when $f=E(z,1/2)$, we also obtain the subconvexity bound \begin{equation*} L(1/2,π)\ll_ε \|μ\|^{3/4-1/4044+ε}. \end{equation*}
