论文标题
subconvex以$ \ textrm {gl（3）} \ times \ textrm {gl（2）} $ $ $ $ l $ - 功能：$ \ textrm {gl（3）} $ - 光谱方面
Subconvex bound for $\textrm{GL(3)} \times \textrm{GL(2)}$ $L$-functions: $\textrm{GL(3)}$-spectral aspect
论文作者
论文摘要
令$ \ $ ϕ $为$ \ mathrm {sl（3，\ mathbb {z}）} $的hecke-maass cusp表格，带有langlands parameters $（{\ bf t} _ {i} _ {i} _ {i}）_ {i = 1} $ \ mathrm {sl（2，\ mathbb {z}）} $。在本文中，我们证明了以下子凸界 $ l \ left（ϕ \ times f，1/2 \ right）\ ll_ {f，ε} 对于$ \ mathrm {gl（3）} $ - 频谱方面，$（{\ bf t} _ {i}）_ {i = 1}^{3} $满足 $$ | {\ bf t} _ {3} - {\ bf t} _ {2} | \ asymp t^{1-ξ}，\ quad \，{\ bf t} _ {i} 使用$ξ$一个真实的数字，因此$ 0 <ξ<1/2 $。
Let $ϕ$ be a Hecke-Maass cusp form for $\mathrm{SL(3, \mathbb{Z})}$ with Langlands parameters $({\bf t}_{i})_{i=1}^{3}$ and $f$ be a holomorphic or Hecke-Maass cusp form for $\mathrm{SL(2,\mathbb{Z})}$. In this article, we prove the following subconvex bound $$ L\left(ϕ\times f, 1/2\right) \ll_{f,ε} T^{ \frac{3}{2}-δ_ξ+ε},\ δ_ξ=\min\{ξ/4, \, (1-2ξ)/4 \}, $$ for the central value $ L\left(ϕ\times f, 1/2\right) $ in the $\mathrm{GL(3)}$-spectral aspect, where $({\bf t}_{i})_{i=1}^{3}$ satisfies $$|{\bf t}_{3} - {\bf t}_{2}| \asymp T^{1-ξ}, \quad \, {\bf t}_{i} \asymp T, \quad \, \, i=1,\,2,\,3,$$ with $ξ$ a real number such that $0 < ξ<1/2$.
