论文标题
subconvexity以$ \ mathrm {gl（3）} \ times \ mathrm {gl（2）} $ $ l $ - functions in $ \ mathrm {gl（gl（2）} $频谱方面
Subconvexity bound for $\mathrm{GL(3)} \times \mathrm{GL(2)}$ $L$-functions in $\mathrm{GL(2)}$ spectral aspect
论文作者
论文摘要
Let $π$ be a Hecke-Maass cusp form for $\mathrm{SL(3, \mathbb{Z})}$ and $f$ be a holomorphic cusp form for $\mathrm{SL(2,\mathbb{Z})}$ of weight $k$ or a Hecke-Maass cusp form corresponding to the Laplacian eigenvalue $ 1/4+k^2 $，$ k \ geq 1 $，对于$ \ mathrm {sl（2，\ mathbb {z}）} $。在本文中，我们证明了以下子范围绑定 \ begin {align*} l \ left（{1}/{2}，\π\ times f \ right）\ ll_ {π，\，\，\，ε} k^{\ frac {3} {2} {2} - \ frac {1} {1} {51} {51}} {51}+ε}。 \ end {align*}
Let $π$ be a Hecke-Maass cusp form for $\mathrm{SL(3, \mathbb{Z})}$ and $f$ be a holomorphic cusp form for $\mathrm{SL(2,\mathbb{Z})}$ of weight $k$ or a Hecke-Maass cusp form corresponding to the Laplacian eigenvalue $1/4+k^2$, $k\geq 1$, for $\mathrm{SL(2,\mathbb{Z})}$. In this paper, we prove the following subconvexity bound \begin{align*} L\left({1}/{2},\ π\times f\right) \ll_{π,\,ε} k^{\frac{3}{2}-\frac{1}{51}+ε}. \end{align*}
